In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides. It does not have curved sides. The sides of a polygon are also called its edges. The points where two sides meet are the vertices (or corners) of a polygon. Show
Here are a few examples of polygons.
Polygon ChartPolygons are named on the basis of the number of sides it has. Polygons are generally denoted by n-gon where n represents the number of sides it has, For example, a five-sided polygon is named as 5-gon, a ten-sided is named as 10-gon, and so on. However, few polygons have some special names. The minimum number of sides a polygon can have is 3 because it needs a minimum of 3 sides to be a closed shape or else it will be open. Even though polygons with sides greater than 10, also have special names, we generally denote them with n-gon as the names are complex and not easy to remember. Types of PolygonThe polygons can be classified on the basis of the number of sides and angles it has:
Regular Polygons – Polygons that have equal sides and angles are regular polygons. For example, an equilateral triangle is a three-sided regular polygon. A square is a four-sided regular polygon. A Regular hexagon is a six-sided regular polygon. Here are a few examples of regular polygons. Irregular Polygons – Polygons with unequal sides and angles are irregular polygons. Here are a few examples of irregular polygons.
Convex Polygons – A convex polygon is a polygon with all interior angles less than 180°. In convex polygons, all diagonals are in the interior of the polygon. (Diagonal is a line segment joining any two non-consecutive vertices of a polygon) Here are a few examples of convex polygons.
In concave polygons, not all diagonals are in the interior of the polygon. Here are a few examples of concave polygons.
Simple Polygon – A simple polygon has only one boundary. The sides of a simple polygon do not intersect. Complex Polygon – Complex polygon is a polygon whose sides cross over each other one or more times. Sum of Angles of a Polygon 1. Sum of the interior angles of a polygon: Sum of the interior angles of a polygon with n sides = (n – 2) × 180° For example: Consider the following polygon with 6 sides Here, ∠a + ∠b + ∠c + ∠d + ∠e + ∠f = (6 – 2) × 180° = 720° (n = 6 as given polygon has 6 sides) 2. Sum of the exterior angles of polygons Sum of the exterior angles of polygons = 360° The sum will always be equal to 360 degrees, irrespective of the number of sides it has. For example: Consider the following polygon with 5 sides Here, ∠m + ∠n + ∠o + ∠p + ∠q = 360° Angles in Regular Polygon In a regular polygon, all its
Interior Angle: Sum of the interior angles of a polygon with n sides = (n – 2) × 180° So, each interior angles = (n – 2) × 180n Exterior Angle: Sum of the exterior angles of polygons = 360° So, each exterior angle = 360°n Sum of Interior Angle and Exterior Angle: Whether the polygon is regular or irregular, at each vertex of the polygon sum of an interior angle and exterior angle is 180°. Solved Examples on PolygonExample 1: Fill in the blank.
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Example 2: Write the number of sides for a given polygon.
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Example 3: Find the measure of each exterior angle of a regular polygon of 20 sides. Solution: The polygon has 20 sides. So, n = 20. Sum of the exterior angles of polygons = 360° So, each exterior angle = 360°n = 360°20 = 18° Example 4: The sum of the interior angles of a polygon is 1620°. How many sides does it have? Solution: Sum of the interior angles of a polygon with n sides = (n – 2) × 180° 1620° = (n – 2) × 180° n – 2 = 1620180 n – 2 = 9 n = 9 + 2 n = 11 So, the given polygon has 11 sides. Practice ProblemsPolygonAttend this Quiz & Test your knowledge. 1 360° 540° 720° 900° CorrectIncorrect Correct answer is: 900° 2 180° 360° 540° 720° CorrectIncorrect Correct answer is: 360° 3 Regular polygon Concave polygon Convex polygon CorrectIncorrect Correct answer is: Concave polygon 4 Square Equilateral triangle Rhombus Hexagon with equal sides CorrectIncorrect Correct answer is: Rhombus Frequently Asked QuestionsWhat is the diagonal of a polygon? A diagonal of a polygon is a line segment connecting two non-consecutive vertices (corners). What are the properties of regular polygons? A Regular polygon has all sides of equal length and each angle also measures equal. Is a circle a polygon? Polygon is a closed shape made up of straight-line segments. The circle is a closed figure but it is made of a curve. So, a circle is not a polygon. What is the minimum number of sides a polygon must-have? A polygon must have a minimum of three sides. Can a number of angles and the number of sides for a polygon be different? No, polygons have the same number of sides and angles because they are closed figures with non-intersecting lines. What are the characteristics of polygon?In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides. It does not have curved sides. The sides of a polygon are also called its edges. The points where two sides meet are the vertices (or corners) of a polygon.
What are 3 examples of a polygon?Triangles, hexagons, pentagons, and quadrilaterals are all examples of polygons. The name gives an indication of how many sides the shape has.
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