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Question 27 The Grammar School at Leeds 11 Pus Maths Entrance Paper 2021

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Learn about Polygons for 11 Plus Exams

1. What are the polygons?

A polygon is a 2D shape with three or more straight sides. Triangles are polygons with three sides, quadrilaterals are polygons with four sides.

For example,

11+ Topicwise Polygons Article Image 01

1.1 Types of polygons

There are two types of polygons: 

[A] Regular polygons: Regular polygons have equal sides and equal interior angles. 

      Example:

11+ Topicwise Polygons Article Image 02

[B] Irregular Polygons: Irregular polygons have different sides and angles. 

      Examples:

11+ Topicwise Polygons Article Image 03

1.2 Diagonals of Polygon

A diagonal of a polygon is a line which joins two non-neighbouring corners. For example, the diagonals for a quadrilateral and a 

11+ Topicwise Polygons Article Image 04

Formula: 

Number of diagonals for an n-sided polygon = n(n - 3) ÷ 2

1.3 Interior and Exterior Angles of polygons

Interior angles are angles formed inside a polygon. Exterior angles are angles formed outside the polygon by extending one side of the polygon. 

For example, 

11+ Topicwise Polygons Article Image 05

The formula to find the interior and exterior angles of the n-sided polygon (regular or irregular):

            Sum of interior angles = (n - 2) × 180°

             Interior angle  = 180° - Exterior angle 

             Exterior angle = 360° ÷ n

             Interior angle  = (n-2) × 180° ÷ n

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