# Find the Number of Diagonals of (Ii) a Polygon of 16 Sides. - Mathematics

Find the number of diagonals of (ii) a polygon of 16 sides.

#### Solution

A polygon of n sides has n vertices. By joining any two vertices we obtain either a side or a diagonal.
∴ Number of ways of selecting 2 out of 9 $=^n C_2 = \frac{n\left( n - 1 \right)}{2}$

Out of these lines, n lines are the sides of the polygon.

∴ Number of diagonals =$\frac{n\left( n - 1 \right)}{2} - n = \frac{n\left( n - 3 \right)}{2}$

There are 16 sides.
∴ Number of diagonals =$\frac{16\left( 16 - 3 \right)}{2} = 104$

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 15.2 | Page 16