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

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is B

$5$

Since the two least prime numbers are $2$ and $3$, thus its sum is $5$.

Also, $5$ is a prime number.

Therefore, the given polygon is a pentagon.

Number of diagonals of a polygon$=\frac{n(n-3)}{2}$ Where $n$ is the number of sides of the polygon

In the case of a pentagon, $n=5$

Number of diagonals of a pentagon$=\frac{5(5-3)}{2}=\frac{5\times 2}{2}=\frac{10}{2}=5$