Question
Download Solution PDFIf the area of a regular pentagon is 3920 \(\sqrt{3} \) cm2, then how long is its each side?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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).
Last updated on Jul 15, 2025
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