If the area of a regular pentagon is 3920 \(\sqrt{3} \) cm², then how long is its each side?

Question

Question

This question was previously asked in

SSC Selection Post 2024 (Higher Secondary Level) Official Paper (Held On: 25 Jun, 2024 Shift 2)

Answer 1

Given:

Area of a regular pentagon = 3920 √(3) cm²

Formula used:

Area of a regular pentagon = (5/4) × a² × cot(π/5)

Where, a = side length

Calculation:

3920 √(3) = (5/4) × a² × cot(π/5)

⇒ a² = (3920 √(3) × 4) / (5 × cot(π/5))

cot(π/5) = √(5 + 2√5)

⇒ a² = (3920 √(3) × 4) / (5 × √(5 + 2√5))

⇒ a² = 15680 √(3) / (5 × √(5 + 2√5))

⇒ a² ≈ 3136

⇒ a ≈ √3136

⇒ a ≈ 56 cm

∴ The correct answer is option (2).

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