Question

Take a regular pentagon and draw all possible diagonals in it. How many different triangles can be formed by the sides of the polygon and its diagonals (as whole segments, not parts of them)?

Answer 1

5 different triangles

Explanation:

we know that

The number of diagonals of an n-sided polygon is given by the formula :

`n(n − 3) / 2`

where

n is the number of sides

In this problem

n=5

substitute

`5(5-3)/2=5\ diagonals`

see the attached figure to better understand the problem

The number of different triangles that can be formed by the sides of the polygon and its diagonals is equal to 5

so

Triangles

AEB

EDC

BCD

ACD

EBC

see the attached figure