NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Multiple Choice Questions
Question 13

Question.  13

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)

7

(D)

10

Detailed Answer with Explanation:

Step 1: Pick the two least consecutive primes.

They are \(2\) and \(3\).

Step 2: Add them to get the number of sides.

\(2 + 3 = 5\). So the polygon has \(n = 5\) sides (a pentagon).

Step 3: Use the diagonals formula.

Number of diagonals of an \(n\)-sided polygon:

\(\text{Diagonals} = \dfrac{n(n-3)}{2}\)

Step 4: Substitute \(n = 5\).

\(\text{Diagonals} = \dfrac{5(5-3)}{2}\)

Step 5: Simplify in small steps.

\(5-3 = 2\)

\(5 \times 2 = 10\)

\(\dfrac{10}{2} = 5\)

Conclusion: The polygon has \(5\) diagonals. Correct option: B (5).

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