Question

A polygon has prime number of sides. Its number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is ______.

Options

• 4

• 5

• 7

• 10

Answer 1

A polygon has prime number of sides. Its number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is 5.

Explanation:

We have given, the number of sides of a polygon = Sum of the two least consecutive primes

= 2 + 3 = 5  .....[∵ 2 and 3 are the least consecutive prime numbers]

∴ The number of diagonals = `(n(n - 3))/2`, where

= `(5(5 - 3))/2 = (5 xx 2)/2` = 5