Question

find the number of diagonals of N sided polygon find the number of diagonals of 8 sided polygon
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Answer 1

Given:

N sided polygon and

8 sided polygon.

To find:

Number of diagonals for each polygon.

Solution:

First of all, let us start with a 3 sided polygon (which is called as a triangle).

A triangle does not have any diagonals.

Now, let us consider 4 sided polygon.

4 sided polygon is known as a quadrilateral and we know that it has 2 number of diagonals.

Now, let us consider a pentagon (5 sided polygon).

It has 5 number of diagonals.

Now, let us consider a hexagon (6 sided polygon).

It has 9 number of diagonals.

Please refer to the attached image for diagrams of a few polygons and their diagonals.

The formula for the number of diagonals of a N sided polygon is given as:

$\bold{\dfrac{N(N-3)}{2}}$

If the polygon is 8 sided, then N = 8

$\dfrac{8(8-3)}{2} = 4\times5 = \bold{20}$