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Example 3: How many diagonals are there in a polygon with 8 sides? Also, draw them.
(
nn − ) 3 A
Solution: We have, the number of diagonals of n-sided polygon = H B
2
Number of diagonals of eight-sided polygon (n = 8) G C
8 ×( 8 3) 85
−
×
= 2 = 2 = 20 F E D
Thus, the number of diagonals in an 8-sided polygon, i.e., in an octagon is 20.

Quick Check

Draw and name the diagonals in the given polygon.
Maths Talk A
Why a triangle does not F B
have any diagonal? Discuss
with your friend or with maths teacher. E C
Give your reason. D

Convex and Concave Polygons

Convex Polygon

Look at the following polygons given below. What do you observe?
A

A D B
E B A C
D
B C D C E
In the polygons, all the diagonals lie in the interior of the polygons. These polygons are known as
convex polygons. In a convex polygon, the measure of each angle is less than 180°.
Concave Polygon

Look at the following polygons given below. What do you observe?

A A
A D
B E E
D
C D

C B C B
At least one of the diagonals of each of the polygons lies in the exterior of the polygon. These
polygons are known as concave polygons. In a concave polygon, the measure of at least one angle
is more than 180°.
Quick Check

Which type of polygons is ?
A convex or a concave polygon

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