Question
Download Solution PDFयदि एक नियमित पंचभुज का क्षेत्रफल 3920 \(\sqrt{3} \) सेमी2 है, तो इसकी प्रत्येक भुजा की लंबाई कितनी है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
एक नियमित पंचभुज का क्षेत्रफल = 3920 √(3) सेमी2
प्रयुक्त सूत्र:
एक नियमित पंचभुज का क्षेत्रफल = (5/4) × a2 × cot(π/5)
जहाँ, a = भुजा की लंबाई
गणना:
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 सेमी
∴ सही उत्तर विकल्प (2) है।
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