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Question: Number of diagonals of an n-sided convex polygon is...

Number of diagonals of an n-sided convex polygon is

A

nC2nC_{2}

B

nC2−1nC_{2} - 1

C

n(n−3)2\frac{n(n - 3)}{2}

D

None

Answer

n(n−3)2\frac{n(n - 3)}{2}

Explanation

Solution

A polygon has n vertices, no three of which are in the same straight line. By joining these points, we get nC2nC_{2} lines as every choice of a pair of points gives us a unique line. These lines include the sides of the polygon. Hence, the number of diagonals.

= nC2−n=n(n−1)∠2−nnC_{2} - n = \frac{n(n - 1)}{\angle 2} - n

= n(n−12−1)=n(n−3)2n\left( \frac{n - 1}{2} - 1 \right) = \frac{n(n - 3)}{2}