A convex polygon has 44 diagonals.


A convex polygon has 44 diagonals. Find the number of its sides. [Hint: Polygon of n sides has (nC2 – n) number of diagonals.]


We know that,


$=\frac{n !}{r !(n-r) !}$

Let the number of sides the given polygon have = n


The number of line segments obtained by joining n vertices = nC2


So, number of diagonals of the polygon = nC– n = 44


n2 – 3n – 88 = 0

(n – 11) (n + 8) = 0

n = 11 or n = – 8

The polygon has 11sides.

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now