# Regular Polygon Questions

24, 25 Homework Help Interior Angles of Regular Polygons Find the measure of an interior angle of the regular polygon. Polygon Questions and Answers - Math Discussion. The Area of a Trapezoid [1/27/1996] My daughter has been assigned to derive the formula for the area. Use your knowledge of the sums of the interior and exterior angles of a polygon to answer the following questions. 180(x-3) + 180 C. This is of course made far more obnoxious by the fact that IsPolygon is a valid rule token, so your rule will seem to be correct, and even pass the rule-checker, but silently fail when you try to actually repour the. Practice questions. 21-23 Example 4: Exs. Ask the class if they agree with where everyone placed their shapes or if they disagree to explain why they think a shape should be moved. Read each question carefully before you begin answering it. Use whatever is shorter in your language. Each interior angle of a regular polygon is the sum of the interior angles of the polygon divided by the number of sides. Is this a inductive reasoning or deductive re. Polygons are multi-sided shapes with different properties. Also, l == [1] * n (1 repeated n times) case is just the regular polygon untouched, which is a valid input. Poly- means "many" and -gon means "angle". Example: How many sides does a regular polygon have if one interior angle. Use Microsoft Paint to create a polygon picture. Name the quadrilaterals shown: rhombus, parallelogram, square, rectangle, or trapezoid. Polygons Questions and Answers - Math Discussion. You can only use the formula to find a single interior angle if the polygon is regular!. Buuuut then you had some questions about the quant section—specifically question 13 of the second Quantitative section of Practice Test 1. Age 11 to 14 Short. Example of how to draw regular polygons using a \foreach loop inside a path. Polygons are two-dimensional, closed, plane shapes composed of a finite number of straight sides that meet at points called vertices. Each student will receive an Area of Irregular Polygons Mini Lesson Examples. 360/x -10x Kudos for the right answer and explanation. Have students come up to the T-chart and place their shapes on the correct side. Enter the number of sides on the polygon. A polygon with the fewest number of sides is a triangle. The moral of this story- While you can use our formula to find the sum of. If you attempt to use geoshape or geotrace questions in forms authored prior to 3. Regular polygon. The problem concerns a polygon with twelve sides, so we will let n = 12. Return from the Polygon Game page to the Math Play homepage. 9 degrees are in the measure of an interior angle of a regular seven sided polygon. Regular Polygons Printable regular polygon sheet which includes picture and name of each of the 10 polygons from triangle, through to dodecagon. Read each question carefully before you begin answering it. Videos, worksheets, 5-a-day and much more. In this video, we'll talk about a few things you need to know about polygons for the GMAT, some of their basic names of regular polygons, and the sum of the interior angles of a polygon. Polygons can be regular or. Polygon diagonals. Find out which polygons are regular and which are not. Polygons problems with solutions for CAT exam. (The other option is to use shape=regular polygon from \usetikzlibrary{decorations. 652 Responses. Download the set (5 Worksheets). The definition of a regular polygons is a polygon that is both equiangular and equilateral. Central angle = 20° Supposing that the polygon is regular, that's all sides are of equal length and all central angles are equal. Formula to find the sum of interior angles of a n-sided polygon is = (n - 2) ⋅ 180 ° By using the formula, sum of the interior angles of the above polygon is = (9 - 2) ⋅ 180 ° = 7 ⋅ 180 ° = 126 0 ° Formula to find the measure of each interior angle of a n-sided regular polygon is. It is the point which is equidistant from each vertex. Unanswered Questions. Angles of Polygons Interior and Exterior Angles of a Polygon After all, there are only so many concepts that are "fair game" on the GMAT, so some questions will be designed to be more difficult by putting these concepts together in unexpected ways. Find the area of a regular hexagon with side length of 10 cm and apothem length of 8. You will have to read all the given answers and click over the correct answer. The number of these congruent triangles is the same as that of its sides. A regular polygon is a polygon that is both equiangular and equilateral. Quiz questions focus on the types of polygons and the. Vocabulary. A regular polygon is a closed, 2-dimensional figure consisting exclusively of line segments of equal length. 6-1 Polygons & Review 29 TEST Friday, 1/25/13 6-1: Properties and Attributes of Polygons I can name polygons with up to ten sides. Consider a random irregular convex polygon, for example, the 6-side polygon I want to define a function that, given a certain parameter r (roundness), rounds each. A regular polygon is a bounded, not self-intersecting polygon in which all edges have the same length and all interior angles are identically, say, $\theta$. 3 of the tikz manual. Regular Polygons A regular polygon has lines that are all the same length and it also has all the same angles. This is part of our collection of Short Problems. Each interior angle of a regular polygon is the sum of the interior angles of the polygon divided by the number of sides. in a kite not all the sides are the same then its angles are not all equal then it is not a regular polygon. A regular polygon has all sides and angles equal (e. Area= (2)(apothem)(perimeter) is the formula for finding the area of a regular polygon. Try to get 100%. My goal is to build a map as this one, where the color represents the number of overlapping polygons, here from 0 to 6:. Level 1 Level 2 Level 3 Exam-Style Description Reminders More Angle Activities Fill in the table with the names and angle sizes of the first eight regular polygons. Practice questions. We can make "pencilogons" by aligning multiple, identical pencils end-of-tip to start-of-tip together without leaving any gaps, as shown above, so that the enclosed area forms a regular polygon (the example above left is an 8-pencilogon). THE NUMBER OF INTERSECTION POINTS MADE BY THE DIAGONALS OF A REGULAR POLYGON BJORN POONEN AND MICHAEL RUBINSTEIN Abstract. I can classify a polygon as concave or convex and regular or irregular. Matching Polygons Matching game for kindergarten, preschool and 1st grade. Includes a number of exercises for which solutions are in the slides. How to use polygon in a sentence. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a straight line. Attempt this quiz as many times as you like. Grade 3 geometry worksheet: Properties of polygons Author: K5 Learning Subject: Grade 3 Geometry Worksheet Keywords: Grade 3 geometry worksheet 2D shapes, lines, angles, parallel, area, perimiter Created Date: 4/28/2017 12:38:52 PM. Start studying True or False polygon questions. Have students come up to the T-chart and place their shapes on the correct side. How many vertices does the following polygon have? Gimme a Hint. You can start playing for free! Polygon Angles - Sample Math Practice Problems The math problems below can be generated by MathScore. all the space on a plane. For example if a polygon has 41 sides, it would be called a 41-gon. …And how about the pentagon…which kinda looks like a home plate. I also make them available for a student who wants to do focused independent study on a topic. Examples of regular polygon: In the adjoining figure of an equilateral triangle ABC there are three sides i. Last week we looked at questions on polygons inscribed in a circle. Convex or Concave Polygons A polygon is either convex or concave. the polygon is the same length and all of its angles have the same degree both equilateral and e Design a class named RegularPolygon that contains: A private int data field named n that defines the number of sides in the polygon. Both equilateral and equiangular conditions are required. Add ScratchPad. † Can any quadrilateral tile the plane? † Can any irregular polygon tile the plane?. Preview and details. Videos, worksheets, 5-a-day and much more. A polygon is called a REGULAR polygon when all of its sides are of the same length and all of its angles are of the same measure. Prepare a Presentation. Grade 3 geometry worksheet: Properties of polygons Author: K5 Learning Subject: Grade 3 Geometry Worksheet Keywords: Grade 3 geometry worksheet 2D shapes, lines, angles, parallel, area, perimiter Created Date: 4/28/2017 12:38:52 PM. The Overflow Blog How to develop a defensive plan for your open-source software project. Find the interior angle sum for each polygon. Now that we’ve been through all of our polygon rules and formulas, let’s look at a few different types of polygon questions you’ll see on the SAT. Coloring Polygons Worksheets. Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser 10. If you're seeing this message, it means we're having trouble loading external resources on our website. Find out which polygons are regular and which are not. Definition of Polygon explained with real life illustrated examples. org are unblocked. Read each question carefully before you begin answering it. A hexagon (six-sided polygon) can be divided into four triangles. Concave polygon. What is the value So, you were trying to be a good test taker and practice for the GRE with PowerPrep online. The dodecagon would have sides of alternating lengths, with ratio $4:\sqrt{12}$; as a specific size for the 30-60-90 triangle is not given. Being equilateral is not enough. Buuuut then you had some questions about the quant section—specifically question 13 of the second Quantitative section of Practice Test 1. 30x+180/x D. Each Interior Angle of a Regular Polygon - MathHelp. Grade 5 Other Polygons CCSS: 5. A regular polygon is one that has equal sides. † Can any quadrilateral tile the plane? † Can any irregular polygon tile the plane?. A "Polygon" object contains the polygon outline. Examples of regular polygons include the equilateral triangle and square. Name the quadrilaterals shown: rhombus, parallelogram, square, rectangle, or trapezoid. User: Approximately how many degrees are in the measure of an interior angle of a regular seven sided polygon? 102. 👍If you like this resource, then please rate it and/or leave a comment💬. Videos, worksheets, 5-a-day and much more. of sides = 360°/20° = 18. We show a quadrilateral and a pentagon below. Regular polygon D. The vertices of an N-vertex polygon are located at the angles (2*Math. a square is a regular quadrilateral). Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. How to use polygon in a sentence. What is the probability that the center of the circle lies inside the. Instructions. Chapter 12. The Corbettmaths Practice Questions on Frequency polygons. The measure of an exterior angle of a convex regular polygon is 45. It is easy to show [39] that there are just five possibilities (vertex figure = triangle, square, tetrahedron, octahedron and cube) and each leads to a unique net. 30x+180/x D. A polygon is a shape that has any number of straight sides, such as a triangle, square or hexagon. Regular polygons have congruent edges and congruent. Central angle = 20° Supposing that the polygon is regular, that's all sides are of equal length and all central angles are equal. I can classify a polygon as concave or convex and regular or irregular. provided a robust regular polygon detection method [4] [5], which derived the α posteriori probability for a mixture of regular polygons and thus the probability density function. A Polygon is a closed figure made up of lines segments (not curves) in two-dimensions. So, if we know all the interior angles other than x, then we can find x. A hexagon has 6 sides. Return from the Polygon Game page to the Math Play homepage. There are 9 polygon maths worksheets. Length = Students who took this test also took : Parallelograms (8. (Must be 18 years old to sign up. Print full size. Area of Polygons Choose the best answer. A polygon in which all the sides are the same length and all the measures have the same measure is regular polygon. Decagons may be irregular or regular. An octagon is any eight-sided polygon, and the sum of its angles is 1080°, as we saw above. If you are not sure about the answer then you can check the answer using Show Answer button. PRACTICE: Polygons – Assignment Worksheet Monday, 1/28/13 6-1: Properties and Attributes of Polygons. A minimum of three line segments are required for making a closed figure, thus a polygon with a minimum of three sides is known as Triangle. The problem concerns a polygon with twelve sides, so we will let n = 12. Selecting Objects Inside Polygon Is there a way within a source drawing to select all objects within a predetermined boundary/polygon? The regular select routine is limited to defining a polygon but not selecting an existing one. The Area of a Trapezoid [1/27/1996] My daughter has been assigned to derive the formula for the area. Similar polygons worksheet answers. Award Information. The simplest polygons are triangles (three sides), quadrilaterals (four sides), and pentagons (five sides). For this lesson, students will find the area of irregular polygons by separating it into smaller identifiable regular polygons. A regular polygon has equal length sides with equal angles between each side. You can now earn points by answering the unanswered questions listed. Instructions. Calculators may be used. Typical Polygon Questions. Irregular polygons are polygons that have unequal angles and unequal sides, as opposed to regular polygons which are polygons that have equal sides and equal angles. 18 sides 8. [1] 6) One interior angle of a regular polygon is 135°. An irregular polygons have sides of differing length and angles of differing measure. So, the above regular polygon has 9 sides. A "Polygon" object contains the polygon outline. Polygons are multi-sided shapes with different properties. In addition to the examples given by Karen: octagons (eight sides), nonagons (nine sides), decagons (ten sides), hendecagons (eleven sides), dodecagons (twelve sides), tridecagons (thirteen sides), tetradecagons (fourteen sides), pendecagons (fift. Do you really know everything about these 2-D polygons and. In these applets, a pentagon and a triangle will be used to illustrate this definition. Learn regular+polygon geometry with free interactive flashcards. How many diagonals does an octagon have?. Question: regular polygon Tags are words are used to describe and categorize your content. Identifying shape attributes, Understanding polygons. The word 'apothem' can also refer to the length of that line segment. Expressions are given for two side lengths. A regular polygon is always convex. Categories of polygons based on the number of sides, and whether they are concave or convex. Show Answer Example 3. Each page is designed with the latest design principles. So a rotation of 72, 144, 216, 288, 360,. Higher Tier. next solving the apothem of octagon. Sum of the interior angles of a polygon = (N - 2) x 180° The number of diagonals in a polygon = 1/2 N(N-3) The number of triangles (when you draw all the diagonals from one vertex) in a polygon = (N - 2) Polygon Parts. Khan Academy is a 501(c)(3) nonprofit organization. Draw the lines of symmetry for each regular polygon, fill in the table including an expression for the number of lines of symmetry in a n-sided polygon. Learn vocabulary, terms, and more with flashcards, games, and other study tools. A Lesson for Kindergarten, First, and Second Grade. In this worksheet, decide whether a polygon is regular or irregular. com, a math practice program for schools and individual families. Polygons are 2-dimensional shapes. All regular star polygons are non-convex polygons. If a regular polygon has x angles each measuring q degrees, then what is the value of q ? A. The Corbettmaths Practice Questions on Frequency polygons. For example, a triangle has 3 sides and 3 angles. Examples of regular polygon: In the adjoining figure of an equilateral triangle ABC there are three sides i. Like 0 Dislike 0 Reply Quote Follow. General Questions: 1. Common Core Standards: Grade 3 Geometry, Grade 4 Geometry. Polygon features One Click Demo Install, so demo content can be installed in minutes. Do you really know everything about these 2-D polygons and. MathScore EduFighter is one of the best math games on the Internet today. Videos, worksheets, 5-a-day and much more. First, take a look at the question itself: The hexagon above has interior angles whose measures are all equal. PRACTICE: Polygons – Assignment Worksheet Monday, 1/28/13 6-1: Properties and Attributes of Polygons. A triangle with all sides and angles equal is known as an equilateral triangle. The following diagram gives the formula to find the area of a regular polygon using the perimeter and the apothem. We also compute the number of regions formed by. I passed my intro programming class with a B because my prof gave us 20 min. 3 A polygon has 2 or more sides and angles. Examples: Regular: Not regular: More Geometry Subjects Circle Polygons Quadrilaterals Triangles Pythagorean Theorem Perimeter Slope Surface Area Volume of a Box or Cube Volume and Surface Area of a Sphere Volume and Surface Area of a. Use MathJax to format equations. Use your knowledge of the sums of the interior and exterior angles of a polygon to answer the following questions. 360/x -10x Kudos for the right answer and explanation. So if we know the sum of the interior angles, we just need to divide that sum by the number of sides to find out the measure of any angle of the polygon: 180(n-2)/n Exterior Angles. A polygon in which all the sides are the same length and all the measures have the same measure is regular polygon. Grade 3 geometry worksheet: Properties of polygons Author: K5 Learning Subject: Grade 3 Geometry Worksheet Keywords: Grade 3 geometry worksheet 2D shapes, lines, angles, parallel, area, perimiter Created Date: 4/28/2017 12:38:52 PM. Convex polygon B. Do you really know everything about these 2-D polygons and. Properties of Decagon. 7) The area of a parallelogram with base of 10 ft and height of 2 ft is 20 square ft. Theorem: The area of a regular polygon. The vertices of an N-vertex polygon are located at the angles (2*Math. This quiz is incomplete! To play this quiz, please finish editing it. All sides are equal length placed around a common center so that all angles between sides are also equal. A polygon is called a REGULAR polygon when all of its sides are of the same length and all of its angles are of the same measure. Access the answers to hundreds of Polygons questions that are explained in a way that's easy for you to understand. In addition to the examples given by Karen: octagons (eight sides), nonagons (nine sides), decagons (ten sides), hendecagons (eleven sides), dodecagons (twelve sides), tridecagons (thirteen sides), tetradecagons (fourteen sides), pendecagons (fift. Many of these shapes, or polygons, can be described as flat closed figures with 3 or more sides. Hand touch global map form lines and polygonal. Here are your FREE materials for this lesson. See our pages on circles and. It is possible to do better than a hexagon, if an irregular polygon is acceptable. A regular polygon is one that has equal sides. A rectangle is a polygon. To know more about different data collection methods, and statistics download BYJU'S -The Learning App. Examples of regular polygon: In the adjoining figure of an equilateral triangle ABC there are three sides i. Polygons come in many shapes and sizes and you will have to know your way around them with confidence in order to ace those SAT questions on test day. Polygons come in many shapes and sizes and you will have to know them inside and out in order to take on the many different types of polygon questions the ACT has to offer. If the measures of a polygon's angles or side lengths differ, then the polygon is called an irregular polygon. Identifying and Describing Polygons All Classroom Lessons. Start by filling in the missing lengths of the sides. The sum of its angles will be 180° × 4 = 720° The sum of interior angles in a hexagon is 720°. Identifying shape attributes, Understanding polygons. Videos, worksheets, 5-a-day and much more. A polygon is a regular polygon if and only if all of its interior angles are equal and all of its sides are of equal length. In this polygon game you will classify different polygons based on their properties. Polygons are 2-dimensional shapes. Combine multiple words with dashes(-), and seperate tags with spaces. In this video I will take you through everything you need to know in order to answer basic questions about the angles of polygons. Irregular polygon C. The number of sides and the radius can be entered via a file, STDIN, or just a plain old variable. 5 (Geometry: n-sided regular polygon) An n-sided regular polygon's sides all have (i. This calculator is designed to give the angles of any regular polygon. Please leave workings so I understand how you get the answer. Let's say you have pixel bitmaps that look something like this: From this I can easily extract a contour, which will be a concave polygon defined by a set of 2D points. Make flat shapes using toothpicks and clay. Before we get too caught up on the excitement of quadrilaterals, let's take time to learn the names and basic properties of different polygons. Updated: Aug 5, 2019. - [Voiceover] So ,a few things…that you should know about polygons,…let's start with the most basic polygon…which is our friend the triangle. Let’s first find the measure of each one of those angles. all of these. In Year 6 children use this knowledge and the following formula to calculate the size of the angles. The sum of the angles of a polygon with n sides, where n is 3 or more, is 180° × (n - 2) degrees. As the concept of irregular polygons is extremely general, knowledge about this concept can be very valuable, both for problem solving and for simple problems in the real world. The simplest regular polygon is the equilateral triangle, which consists of three edges of equal length and three angles between each pair of edges to be 60 degrees. Consider, for instance, the ir regular pentagon below. How many sides does an octagon have? eight 2. Creating Polygons - investigating the Concept of Triangle and the Properties of Polygons ( from NCTM ) ; Figures and Polygons - definitions and examples of a large number of figures fiting the definition of polygon ; Identify Polygons - names of polygons by number of. For the regular polygons inscribed in the unit circle, what is the range of values that the apothem can have?. Higher Tier. Please leave workings so I understand how you get the answer. Examples of regular polygon: In the adjoining figure of an equilateral triangle ABC there are three sides i. shapes}; see section 51. A polygon is regular, if all its sides have the same length and all its angles have the same measure. , AB, BC and CA are equal and there are three angles i. Abstract polygon. If a polygon is regular, there is a point which we can define as the center. Then ask guiding questions to see if they recognize the pattern (every time you add a side, the interior angle sum increases by 180°). Our online polygon trivia quizzes can be adapted to suit your requirements for taking some of the top polygon quizzes. A regular three-sided polygon is called an equilateral triangle. An Apothem is a line segment from center point of side of a regular polygon to the midpoint of the regular polygon. Categories & Grades. 1) heptagon 2) decagon 3) nonagon 4) hexagon 5) pentagon 6) nonagon 7) hexagon 8) nonagon State if each polygon is concave or convex. † Can any quadrilateral tile the plane? † Can any irregular polygon tile the plane?. A square is a rhombus. " Knowing the names of the polygons is only the start. Feel free to always add Asymptote solution to any questions related to plotting, drawing, diagramming, etc because it is allowed by law in this site. Indeed, it is clear, that under the given conditions, a regular triangle is the only possible regular polygon with the smaller interior angle. Each student will receive an Area of Irregular Polygons Mini Lesson Examples. Choose from the following regular polygons: Triangle,. Test comprehension with the questions that follow. A regular polygon has sides which are all the same length as well as angles which are all the same. Regular Polygon. Browse other questions tagged tikz-pgf or ask your own question. A regular polygon is one that has equal sides. Polygons can be regular or. Khan Academy is a 501(c)(3) nonprofit organization. Abstract background with polygonal shapes. 25 Mocks + 30 Sectionals for Rs. 7) The area of a parallelogram with base of 10 ft and height of 2 ft is 20 square ft. You can tell, just by looking at the picture, that $$\angle A and \angle B$$ are not congruent. The shape on the left has equal sides and angles, so it is a regular polygon. 👍If you like this resource, then please rate it and/or leave a comment💬. Questions for Students. A regular polygon is a closed, 2-dimensional figure consisting exclusively of line segments of equal length. Polygon abstract background. Exterior angle = 180-178 = 2° because the interior and exterior angle together make a straight line. If a regular polygon has x sides, then the degree measure of each exterior angle is 360 divided by x. The sum of the exterior angles of any polygon is 360°. If none of the sides, when extended, intersects the polygon, it is a convex polygon; otherwise it is concave. What is the latest version of SketchUp that Keyframe Animation will work with?. In this polygon game you will classify different polygons based on their properties. The applets below illustrate what it means for any polygon to be classified as a regular polygon. 9 degrees are in the measure of an interior angle of a regular seven sided polygon. A Polygon is a 2D shape which is made up of straight line segments. In our example, it's equal to 5 in. Start studying Quadrilateral & Polygon Unit Review Questions. Fortunately, as you'll see in the following practice questions, there's a handy formula that you can use to find a missing interior angle in a […]. We can make "pencilogons" by aligning multiple, identical pencils end-of-tip to start-of-tip together without leaving any gaps, as shown above, so that the enclosed area forms a regular polygon (the example above left is an 8-pencilogon). Convex polygon B. The resulting polygon is guaranteed to be simple (it does not intersect or touch itself). It is the point which is equidistant from each vertex. Upgrade your subscription to get access to this quiz, more lessons, and more practice questions. polygon: a 2D or flat, closed shape with straight sides. A regular polygon is a polygon whose sides are equal length and whose angles are all the same value. Polygons are 2-dimensional shapes with straight sides. Area= (2)(apothem)(perimeter) is the formula for finding the area of a regular polygon. Work out the identity of the missing regular. Tutors Answer Your Questions about Polygons (FREE) Get help from our free tutors ===> Algebra. Name the quadrilaterals shown: rhombus, parallelogram, square, rectangle, or trapezoid. Upgrade your subscription to get access to this quiz, more lessons, and more practice questions. Here we look at Regular Polygons only. I can classify a polygon as concave or convex and regular or irregular. The sum of the angles of a polygon with n sides, where n is 3 or more, is 180° × (n - 2) degrees. To do so, I would like to construct an irregular polygon, and from each of it's sides, construct a *regular* n-gon, on the outside of the irregular-gon. Sample Problem 4: Draw a figure that fits the description. Selecting Objects Inside Polygon Is there a way within a source drawing to select all objects within a predetermined boundary/polygon? The regular select routine is limited to defining a polygon but not selecting an existing one. This quiz will focus on different shapes classified as polygons. t = 360 o / 12 = 30 o; We now use the formula for the area when the side of the regular polygon is known Area = (1 / 4) n x 2 cot (180 o / n) Set n = 12 and x = 6 mm area = (1 / 4) (12) (6 mm) 2 cot (180 o / 12). One interior angle of a regular polygon - (n - 2). Diagonals of a Regular Octagon. Can be “regular” – all sides and all angles are equal to each other Two sides of equal length Three acute angles Sum of angles = 180° All sides equal length Three acute angles Sum of angles = 180° Is a regular polygon No sides are equal No angles are equal May have obtuse angle Sum of angles = 180 ° Opposite sides are parallel Opposite. A polygon is a shape that has any number of straight sides, such as a triangle, square or hexagon. Polygon or Not? This Is the Question : In this game, students will quickly decide whether a geometrical figure is a polygon or not a polygon. Round your answer to the nearest tenth if necessary. For the Independent Practice students will use the area formulas to help them complete the Finding the Finding the Area of Regular Polygons Worksheet. This is of course made far more obnoxious by the fact that IsPolygon is a valid rule token, so your rule will seem to be correct, and even pass the rule-checker, but silently fail when you try to actually repour the. Mathematics (Linear) - 1MA0 ANGLES: POLYGONS Answer the questions in the spaces provided - there may be more space than you need. A clock is constructed using a regular polygon with 60 sides the polygon rotates every minute how has the polygon rotated after 7 minutes. Using the area of regular polygon calculator: an example. Videos, worksheets, 5-a-day and much more. The angles have been calculated manually. Polygons are multi-sided shapes with different properties. Videos, worksheets, 5-a-day and much more. Solve these reasoning questions. 2019 23:53, kumarivishakha118. Always show your workings. A three-sided polygon is called a triangle. A regular polygon is both equilateral and equiangular. SplashLearn is an award winning math learning program used by more than 30 Million kids for fun math practice. The formula is (n - 2) times 180 divided by n , where n is the number of sides. Find the area of each of the following regular polygons. The outline itself is matched with the InPolygon rule (which is what you want). Area of Polygons. parallel lines: two lines that are always the same distance apart and never touch. They should not be confused with regular polygons. Is this a inductive reasoning or deductive re. A "Regular Polygon" has: all sides equal and. The only constructible regular polygons with an odd number of sides are those for which this number is a product of distinct Fermat primes (so for instance 15 = 3 times 5, 51 = 3 times 17), and the only ones with an even number of sides are those obtained by repeatedly doubling these numbers (including 1), thus:- (1,2), 4, 8, 16, 32, 64,. true false. The sum of the angles of a polygon with n sides, where n is 3 or more, is 180° × (n - 2) degrees. (Must be 18 years old to sign up. 1) 2) 3) regular 19-gon 4) regular 14-gon Find the measure of one exterior angle in each regular polygon. A polygon is called a REGULAR polygon when all of its sides are of the same length and all of its angles are of the same measure. The area of the regular polygon is 297 m 2. 2D SHAPES > REVISION > GCSE QUESTIONS. If someone can help me out that would be awesome. Videos, worksheets, 5-a-day and much more. Unit 7 Test Polygons And Quadrilaterals Answer Key. Unanswered Questions. A brief description of the worksheets is on each of the worksheet widgets. A "Polygon" object contains the polygon outline. A diagonal of a polygon is any line segment that connects non-consecutive vertices of the polygon. Expressions are given for two side lengths. Award Information. Menu Skip to content. [1] 6) One interior angle of a regular polygon is 135°. The measure of an exterior angle of a convex regular polygon is 45. A polygon is regular, if all its sides have the same length and all its angles have the same measure. This figure shows the most common polygons. Improve your math knowledge with free questions in "Interior angles of polygons" and thousands of other math skills. Geometry Polygons questions and answers for CAT. 652 Responses. A polygon is irregular, if it is not regular. Hint: 360/No. A polygon in which all the sides are the same length and all the measures have the same measure is regular polygon. I will be focusing on convex regular. Download the set (5 Worksheets). TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. You will have to read all the given answers and click over the correct answer. An n-sided regular polygon is rotationally symmetric around its centre. In Year 6 children use this knowledge and the following formula to calculate the size of the angles. Tags: Question 40. A regular polygon is a polygon all of whose sides are of the same length (equilateral) and all of whose internal angles are the same (equiangular). A polygon that is not a regular polygon is called an irregular polygon. Classify the polygon by the number of sides. Chapter 12. all angles equal. As a child, there's a point in life where shapes and what we now have come to refer as "geometry" are the most fascinating things in the world. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. ) Sign Up More Info Close. disproportional perimeters. As an example: A pentagon has five sides, 360/5 =72. This figure shows the most common polygons. If you are not sure about the answer then you can check the answer using Show Answer button. Type all answers in the boxes provided. Polygons Exercises ; Topics Which of the following look like regular polygons? Gimme a Hint. The size of each of the interior angle of a regular polygon = (n-2) x 180º ÷ n Where n is the number of sides. You Try It! How many sides does a regular polygon have if each interior angle measures 160 ? Example 5: Solving Algebraic Problems Find the value of x. I can classify a polygon as concave or convex and regular or irregular. (Construct it from scratch, or use a script. You will have to read all the given answers and click over the correct answer. We can see from the above examples that the number of triangles in a polygon is always two less than the number of sides of the polygon. A brief description of the worksheets is on each of the worksheet widgets. Polygons Author: act Last modified by: act Created Date: 7/10/2008 4:49:14 PM Document presentation format: On-screen Show (4:3) Other titles: Corbel Arial Wingdings 2 Wingdings Wingdings 3 Calibri Module 1_Module 2_Module 3_Module 4_Module 5_Module 6_Module Polygons What is a polygon?. An octagon is any eight-sided polygon, and the sum of its angles is 1080°, as we saw above. You can tell, just by looking at the picture, that $$\angle A and \angle B$$ are not congruent. PI*K)/N where K goes from 0 to N-1, inclusive. The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. Main Ideas/Questions POLYGON Notes/Examples A polygon isa figure formed by three or more line Date: Class: hexagon? EXAMPLES 9. 180(x-3)/x B. Formula for the sum of interior angles. A convex polygon has no angles pointing inwards. s = (160cm)/8 = 20 cm. Two congruent figures have equal areas. Print full size. Examples of regular polygons include the equilateral triangle and square. 652 Responses. What is the latest version of SketchUp that Keyframe Animation will work with?. To find the perimeter of a polygon, add the lengths of its sides. If none of the sides, when extended, intersects the polygon, it is a convex polygon; otherwise it is concave. This is part of our collection of Short Problems. Formula to find the sum of interior angles of a n-sided polygon is = (n - 2) ⋅ 180 ° By using the formula, sum of the interior angles of the above polygon is = (9 - 2) ⋅ 180 ° = 7 ⋅ 180 ° = 126 0 ° Formula to find the measure of each interior angle of a n-sided regular polygon is. There are multiple ways to found the Apothem of a Regular Polygon. I can find the measure of an interior angle of any regular polygon. Background polygon. You can now earn points by answering the unanswered questions listed. Background polygon. The applets below illustrate what it means for any polygon to be classified as a regular polygon. A polygon is irregular, if it is not regular. Along with it, the property of equal-length sides, this implies that every regular polygon also has an inscribed circle or incircle that is tangent to every side at the midpoint. (Construct it from scratch, or use a script. org are unblocked. Diagonals of a Regular Octagon. The vertices of an N-vertex polygon are located at the angles (2*Math. Identifying and Describing Polygons All Classroom Lessons. The sum of the exterior angles of any polygon is 360 degrees. What is the minimum interior angle possible for a regular polygon or why. A worksheet on angles in polygons. A Ogee curve is a _____ a) semi ellipse b) continuous double curve with convex and concave c) freehand curve which connects two parallel lines d) semi hyperbola View Answer. A polygon is a plane shape (two-dimensional) with straight sides. Tell whether the polygon is equilateral, equiangular, or regular. 2nd and 3rd Grades. Interact with these applets for a minute or two, then answer the questions that follow. of sides = Interior angle Attempt drawing a pentagon on your own first. A convex polygon has no angles pointing inwards. Concave polygon. A regular polygon is a polygon that is both equilateral and equiangular (having both. Polygon abstract background. All photos are included but can be easily changed to match your branding’s style and personality. Assume that the regular polygon has n sides (or angles). A regular polygon is a polygon all of whose sides are of the same length (equilateral) and all of whose internal angles are the same (equiangular). Solution to Problem 2: Let t be the size of angle AOB, hence t = 360 o / 5 = 72 o; The polygon is regular and OA = OB. Add ScratchPad. For example if a polygon has 41 sides, it would be called a 41-gon. The Corbettmaths Practice Questions on Frequency polygons. …And how about the pentagon…which kinda looks like a home plate. Each question will change subtly every time you take. The number of sides is also the number of angles and, in a regular polygon, all the angles are the same. Expressions are given for two side lengths. (Remade and reuploaded 9th February 2020) Calculating interior and exterior angles of polygons. Making statements based on opinion; back them up with references or personal experience. Grade 3 geometry worksheet: Properties of polygons Author: K5 Learning Subject: Grade 3 Geometry Worksheet Keywords: Grade 3 geometry worksheet 2D shapes, lines, angles, parallel, area, perimiter Created Date: 4/28/2017 12:38:52 PM. Find the area of the regular polygon. Sample Problem 5: Each figure is a regular polygon. of sides = 360°/20° = 18. So, if we know all the interior angles other than x, then we can find x. polygons Questions #1 Relates the number of sides, angles, and vertices of a polygon Question #2 Describes attributes of polygons Question #3 Wow! Thoroughly describes. Shape And Formula Of A Polygon Quiz 10 Questions | By Swords31535 | Last updated: Oct 11, 2017 | Total Attempts: 9314 All questions 5 questions 6 questions 7 questions 8 questions 9 questions 10 questions. You may also be interested in our longer problems on Angles, Polygons and Geometrical Proof Age 11-14 and Age 14-16. Regular Polygons Printable regular polygon sheet which includes picture and name of each of the 10 polygons from triangle, through to dodecagon. A polygon is a flat shape with straight sides that are joined to form a closed shape. You will have to read all the given answers and click over the correct answer. 1) 2) 3) regular 19-gon 4) regular 14-gon Find the measure of one exterior angle in each regular polygon. Although students should work independently, they may want to discuss or ask questions of their group. An n-sided regular polygon is rotationally symmetric around its centre. A regular polygon is always convex. I can solve reasoning questions about comparing, classifying and finding unknown angles in polygons. no space at all. Design a class named RegularPolygon that contains: Aprivate int data field named n that defines the number of sides in the polygon with default value 3. where n - number of sides of octagon. Irregular polygons are polygons that have unequal angles and unequal sides, as opposed to regular polygons which are polygons that have equal sides and equal angles. How many angles does a triangle have? three 3. While we are given two sides - the base and the height - we do not know the hypotenuse. com Regular Polygons Grade 3 Geometry Worksheet Answers: Color the regular quadrilateral. Questions and Facts † What are the only edge-to-edge regular tilings? That is, what regular polygons allow for edge-to-edge tiling of the plane? † Can we use more than one regular polygon, with different number of size, to tile the plane edge-to-edge? † Any triangle can tile the plane. Here we look at Regular Polygons only. Improve your math knowledge with free questions in "Regular and irregular polygons" and thousands of other math skills. Note that the polygon we are given is not a regular polygon, since the side lengths are not all equal. In a regular octagon, each angle = 1080°/8 = 135° That angle is the supplement of a 45° angle. To find the perimeter, multiply the length of one side by the total number of sides. In this video, we'll talk about a few things you need to know about polygons for the GMAT, some of their basic names of regular polygons, and the sum of the interior angles of a polygon. Draw all of the diagonals in each regular polygon. Two congruent figures have equal areas. angles of polygons section 8-1 jim smith jchs names of polygons sides triangle 3 quadrilateral 4 pentagon 5 hexagon 6 heptagon 7 octagon 8 nonagon 9 decagon 10 dodecagon 12 n - gon n interior angle sum each triangle has 180° if n is the number of sides then: int angle sum = (n - 2 ) 180° angles of polygons section 8-1 names of polygons sides triangle 3 quadrilateral 4 pentagon 5 hexagon. Restate for the class a clear definition of polygon: a 2D or flat, closed shape with straight sides. Formula for the sum of interior angles. The moral of this story- While you can use our formula to find the sum of. Polygon features One Click Demo Install, so demo content can be installed in minutes. I usually print these questions as an A5 booklet and issue them in class or give them out as a homework. There can't be a better way to introduce polygons, than what kids love the most - coloring! Direct kids to follow the color key provided to identify polygons like triangles, quadrilaterals, pentagons and more. A regular polygon has an exterior angle of 20 degrees. com For a complete lesson on regular polygons, go to https://www. The simplest regular polygon is the equilateral triangle, which consists of three edges of equal length and three angles between each pair of edges to be 60 degrees. Find the area of each regular polygon. The shape on the left has equal sides and angles, so it is a regular polygon. ) The area formula for a regular polygon is 1/2ap. $$\therefore$$ the area of one such triangle $$= \frac{1}{2} \times$$ sides of polygon $$\times$$ length of perpendicular from the center to any side of. 2D SHAPES > REVISION > GCSE QUESTIONS. The vertical coordinate can be calculated as a sine of the angle times the radius of the circumcircle; the horizontal coordinate is calculated the same way, except you need to multiply the radius by the cosine of the angle. In this regular polygon lesson plan, 10th graders find the area of a regular polygon in terms of the apothem and the perimeter. Regular Polygon. The regular polygons were known to the ancient Greeks, and the pentagram, a non-convex regular polygon (star polygon), appears on the vase of Aristophonus, Caere, dated to the 7th century B. Using the area of regular polygon calculator: an example. t = 360 o / 12 = 30 o; We now use the formula for the area when the side of the regular polygon is known Area = (1 / 4) n x 2 cot (180 o / n) Set n = 12 and x = 6 mm area = (1 / 4) (12) (6 mm) 2 cot (180 o / 12). The sum of the exterior angles of any polygon is 360 degrees. A Polygon is a 2D shape which is made up of straight line segments. Browse other questions tagged qgis polygon intersection or ask your own question. Polygons maths worksheet 3 accurately completes the polygons. 6 9 52) 14 14. A regular polygon has sides of equal length, and all its interior angles are of equal size. A regular polygon have the number of lines of symmetry equal to the number of sides of the regular polygon. The dodecagon would have sides of alternating lengths, with ratio $4:\sqrt{12}$; as a specific size for the 30-60-90 triangle is not given. Label the sides and angles on each polygon. Sum of interior angles = 180 (n – 2) where n = the number of sides in the polygon. A polygon is a 2D shape with at least three sides. A regular polygon has sides which are all the same length as well as angles which are all the same. a positive number representing the interior space of a polygon. all of these. Categories & Grades. Kahoot! is a free game-based learning platform that makes it fun to learn - any subject, in any language, on any device, for all ages! Unit 7 test polygons and quadrilaterals answer key. 25 Mocks + 30 Sectionals for Rs. If a regular polygon has x angles each measuring q degrees, then what is the value of q ? A. In geometry, polygons cover a lot of ground, so you can bet that some questions on the ACT Math exam will involve polygons—specifically, finding the interior angles of a polygon. This calculator is designed to give the angles of any regular polygon. Always show your workings. White neural texture abstract vector. Khan Academy is a 501(c)(3) nonprofit organization. Let's say you have pixel bitmaps that look something like this: From this I can easily extract a contour, which will be a concave polygon defined by a set of 2D points. of sides = 360°/20° = 18. The sum of the exterior angles of any polygon is 360°. An irregular polygons have sides of differing length and angles of differing measure. Find the value of. The following figures are polygons. Find the length of one side. Support your method with examples. This quiz is incomplete! To play this quiz, please finish editing it. Updated: Aug 5, 2019. (n – 2)*180 = sum of all interior angles (6 – 2)*180 = 720. There are various ways to solve this question, but each takes a bit of effort. For a polygon to be 'regular' it must have. Each angle in a regular decagon is equal to 144°. How to find the interior angle of a regular polygon. Polygons are two-dimensional objects, not solids. tells you the sum of the interior angles of a polygon, where n represents the number of sides. Polygons are 2-dimensional shapes. A polygon is called a REGULAR polygon when all of its sides are of the same length and all of its angles are of the same measure. x1, x2 ,y1 ,y2. com for more resources, like predicted GCSE Maths Papers, Topic Buster and challenge yourself against our Demon questions. The formula. This quiz will focus on different shapes classified as polygons. A triangle is a 3 sided polygon with interior angles that add to 180 degrees. In these applets, a pentagon and a triangle will be used to illustrate this definition. Question 1. Identifying and Describing Polygons All Classroom Lessons. Regular polygons. There can't be a better way to introduce polygons, than what kids love the most - coloring! Direct kids to follow the color key provided to identify polygons like triangles, quadrilaterals, pentagons and more. Area of Regular Polygons If radii are drawn from the center of a regular polygon to the vertices, congruent isosceles triangles are formed. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a straight line. Regular Polygon Formulas. Illustrated with examples of polygons in everyday life. Newest Active Followers. 120° ° 85° 53° 115° x° 117° 105° 120. In geometry, polygons cover a lot of ground, so you can bet that some questions on the ACT Math exam will involve polygons—specifically, finding the interior angles of a polygon. A hexagon (six-sided polygon) can be divided into four triangles. The interactive lessons include: Polygons and Non-Polygons in which students will drag a series of shapes to either the bucket that says polygon or the bucket that says non-polygon. A rectangle is a special quadrilateral where opposite sides are congruent-- that is, the same length -- and each angle is a right angle. Expected time to solve, similar questions of 11 Plus exam practice papers. Find the length of one side. This is of course made far more obnoxious by the fact that IsPolygon is a valid rule token, so your rule will seem to be correct, and even pass the rule-checker, but silently fail when you try to actually repour the. Area is the negative space inside a polygon. A comprehensive database of more than 34 polygon quizzes online, test your knowledge with polygon quiz questions. +34,000 Free Graphic Resources. Figure 4 – The Interior angles of polygons that can tessellate the plane add up to 360 degrees. The sum of the exterior angles of any polygon is 360 degrees. I also make them available for a student who wants to do focused independent study on a topic. The polygon is a 18-sided regular polygon; a regular octadecagon. A worksheet on angles in polygons. I want to find the direction of s. Published on Jan 20, 2017. In Year 6 children use this knowledge and the following formula to calculate the size of the angles. See our pages on circles and. So if we know the sum of the interior angles, we just need to divide that sum by the number of sides to find out the measure of any angle of the polygon: 180(n-2)/n Exterior Angles. A regular net is defined as one in which the vertex figure is required by symmetry to be a regular polygon or polyhedron. Polygons maths worksheet 4 and polygon maths worksheet 5 work with tessellation. (n – 2)*180 = sum of all interior angles (6 – 2)*180 = 720.


What's $1^3+2^3+3^3+\cdots+99^3$ modulo $3$?

What's the remainder when the sum

$$1^3+2^3+3^3+\cdots+99^3$$ is divided by $$3$$?

Background:

I saw this question on MSE but it was closed and I wanted to learn how to approach it. The help given to the asker had failed to bring the question up to an acceptable standard.

I can solve it but I doubt my methods are efficient.

One way is to start by removing every third term. Then the first two terms of the remaining sequence can be removed, and so on... a pattern may emerge.

Another way is to look at the expansion of $$(x+1)^3$$ and see what it does to the residues for each $$x$$, then sum over that by induction.

But I'm sure my inventions aren't very efficient.

• Use $n^3\equiv n\pmod3$. – Angina Seng Dec 27 '18 at 5:42
• math.stackexchange.com/questions/1328798 – Andrei Dec 27 '18 at 5:43
• In general, note that you can handle the terms in groups of $3$ as $n + 3 \equiv n \pmod 3$, and also use that $n^3 \equiv n \pmod 3$ as Lord Shark the Unknown stated above. – John Omielan Dec 27 '18 at 5:46
• @LordSharktheUnknown ah thanks. I guess the $(x+1)^3$ method would've revealed that. – samerivertwice Dec 27 '18 at 5:46

By Fermat's little theorem $$a^3\equiv a\pmod3$$. Then you have $$\sum_{k=1}^{99} k=\frac{(99)(100)}2=50\cdot 99\equiv 0\pmod3$$.

\begin{align} \sum_{i=1}^{99}i^3 &= \sum_{i=0}^{32} (3i+1)^3 + \sum_{i=0}^{32} (3i+2)^3 + \sum_{i=0}^{32} (3i+3)^3 \\ &\equiv \sum_{i=0}^{32} 1^3 + \sum_{i=0}^{32} 2^3 + \sum_{i=0}^{32} 0^3 \pmod{3}\\ &\equiv \sum_{i=0}^{32} 1^3 + \sum_{i=0}^{32} (-1)^3 + \sum_{i=0}^{32} 0^3 \pmod{3}\\ &\equiv 0 \pmod{3} \end{align}

Split the numbers from $$1,\ldots, 99$$ in

• $$33$$ with remainder $$1$$
• $$33$$ with remainder $$2$$
• $$33$$ with remainder $$0$$ $$1^3 + 2^3 + \cdots + 99^3 \equiv 33\cdot (1^3+2^3+0^3) \equiv 0 \mod 3$$

consider these observations:

$$1 = 1 \pmod 3$$ $$2 = -1 \pmod 3$$ $$3 = 0 \pmod 3$$

This becomes:

$$33(1^3+(-1)^3+0) \equiv 33(1+(-1)+0) \equiv 33(0) \equiv 0 \pmod 3$$

Hint:

$$n^3\equiv n\pmod3$$ as $$n^3-n=n(n-1)(n+1)$$ is the product of three consecutive integers

We have $$\sum_{r=1}^mr^3\equiv\sum_{r=1}^mr\pmod3$$

$$\equiv \dfrac{m(m+1)}2$$

Alternatively $$\sum_{r=1}^m r^3=\dfrac{m^2(m+1)^2}4$$

From $$a^{3} + b^{3} = (a+b)(a^{2}-ab+b^{2})$$, you have $$a+b|a^{3} +b^{3}$$ and \begin{align} &1^{3} + 2^{3} + 3^{3} + \cdots + 97^{3} + 98^{3} + 99^{3} \\ &= (1^{3} + 2^{3}) + (4^{3} + 5^{3}) + \cdots + (97^{3}+98^{3}) + (3^{3}+6^{3} + \cdots + 99^{3}) \end{align} is a multiple of 3.

Another method is to use the identity

$$\sum_{k=1}^nk^3=\left(\sum_{k=1}^nk\right)^2$$ So, $$\sum_{k=1}^{99}k^3\equiv\left(\sum_{k=1}^{99}k\right)^2\equiv\frac{(99)^2(100)^2}{4}\equiv0\ (\mod3)$$

Yet another method is to use that $$(x-1)^3=x^3-3x^2+3x-1$$ and $$(x+1)^3=x^3+3x^2+3x+1$$, so $$(x-1)^3+x^3+(x+1)^3 = 3x^3+6x$$, which is divisible by three. This shows that any three consecutive numbers, when cubed, add up to zero modulus three.

You can also calculate that sum using

$$\sum_{i=0}^{i=n}i^3=\dfrac{n^2(n+1)^2}{4}$$

Here: $$\sum_{i=0}^{i=99}i^3=\dfrac{99^2(99+1)^2}{4}$$ which is clearly divisible by 3.


Contest Duration: - (local time) (100 minutes) Back to Home
Official

## B - log2(N) Editorial by en_translator

There are various approaches to solve this problem. Here, we will explain some of them. Even if you got accepted during the contest, we recommend considering other solutions.
Note that the sample codes in this editorials are provided in C++.

1. Basic solution
2. Solution using logarithmic function, and numerical errors
3. Solution using binary representation of an integer

#### 1. Basic solution

First, as $$k$$ increases, obviously $$2^k$$ gets larger too. Therefore, we can see that $$2^k \le N$$ for all integers $$k$$ up to some boundary, or $$2^k>N$$ for $$k$$ greater than that value.
Thus, we can find the answer with a loop where $$k$$ is incremented one by one .
Note that one can $$2^k$$ efficiently compute $$2^k$$ during the loop of incrementing $$k$$ for a good computational complexity.

#include<bits/stdc++.h>

using namespace std;

int main(){
long long n;
cin >> n;
long long val=1;
for(long long i=0;i<=60;i++){
if(val>n){
cout << i-1 << '\n';
break;
}
val*=2;
}
return 0;
}

#### 2. Solution using logarithmic function, and numerical errors

By applying logarithmic function to $$2^k \le N$$ we obtain $$k \le \log_2(N)$$. Therefore, one should be able to output the $$\log_2(N)$$, rounded down to an integer, to get accepted.
However, this code results in WA (Wrong Answer).

#include<bits/stdc++.h>

using namespace std;

int main(){
long long n;
cin >> n;
cout << floor(log2(n)) << '\n';
return 0;
}

The cause of WA is lack of precision. Specifically, a precision occurs for the following case ($$N=2^{59}-1$$). (WA: 59, AC: 58)

576460752303423487

In order to avoid the error, one can use a type having more precisions than 64-bit floating point decimal. If you modify the last code as follows, you can get accepted for this problem.

#include<bits/stdc++.h>

using namespace std;

int main(){
long long n;
cin >> n;
cout << floor(log2((long double)n)) << '\n';
return 0;
}

No that high-precision type is not always omnipotent. If the constraints for this problem were $$N \le 2 \times 10^{18}$$, the modified code still outputs a wrong answer for the following test case. (WA: 60, AC: 59)

1152921504606846975

In competitive programming, discarding the integral property in an integral problem and using only decimals is dangerous. We recommend you to process integral problems in integer-typed values as much as possible. When you inevitably use decimals, be very careful about the errors.

#### 3. Solution using binary representation of an integer

Consider the binary representation of the integer.
For example, we have the conversions $$6=110_{(2)}$$ and $$15=1111_{(2)}$$.
Here, the inequality $$2^{k} \le N < 2^{k+1}$$ can be transformed into binary notations as follows.
$$1 \underbrace{ 00 \dots 0 }_{ k }\ _{(2)} \le N < 1 \underbrace{ 00 \dots 0 }_{ k+1 }\ _{(2)}$$
Using this property, we can derive the following solution.

• If the binary notation of $$N$$ (without leading $$0$$’s) has $$k$$ digits (that is, if the most significant bit with value $$1$$ is the $$k$$-th least significant bit), then the answer is $$k-1$$.

There are various ways to implement this, while using bit operations simplifies it. (Note that the least significant digit is treated as the $$0$$-th digit.)

#include<bits/stdc++.h>

using namespace std;

int main(){
long long n;
cin >> n;
for(int i=60;i>=0;i--){
if(n&(1ll<<i)){cout << i << '\n';break;}
}
return 0;
}

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