Question

Find the number of diagonals of :

A polygon of 16 sides.

Answer 1

A polygon of 16 sides 

We have given that polygon has 16 vertices and each side and diagonal can be formed by joining two vertices of a polygon, 

Let us assume the no. of diagonals of the polygon are N, 

⇒ N = (no. of lines formed on joining any two vertices) – (no. of sides of the polygon) 

⇒ N = ¹⁶C₂ – 16 

We know that,

ⁿC_r = \(\frac{n!}{(n-r)!r!}\)

And also,

n! = (n)(n – 1)......2.1

⇒ N = 120 – 16 

⇒ N = 104 

∴ The total no. of diagonals formed are 104.