# Find The Number of Sides of Polygon ?

The polygon has 44 diagonals. The number of its sides is

- 11
- 10
- 8
- 7

**Answer: (1) 11**

**Explanation:-
**

**Formula –**

**The number of diagonals in a polygon = [n(n – 3)]/2**

Where, n = number of sides of polygon

Where, n = number of sides of polygon

Then, 44 = n (n – 3)/2

44 = [ n^2 – 3 n]/2

by cross multiplication,

2 x 44 = n^2 – 3 n

n^2 – 3 n – 88 = 0

n^2 – 11 n + 8 n – 88 = 0

n (n – 11) + 8 (n – 11) = 0

n – 11 = 0

n = 11

Then, the number of sides of the polygon is 11.

Hence, the answer is (1) 11.