Question
Download Solution PDFएक समकोण प्रिज्म का आधार समबाहु त्रिभुज है जिसकी भुजा 10 सेमी है। यदि इस प्रिज्म की ऊँचाई 10\(\sqrt{3}\) सेमी है, तो प्रिज्म का कुल पृष्ठीय क्षेत्रफल कितना है?
Answer (Detailed Solution Below)
Detailed Solution
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एक समकोण प्रिज्म का आधार एक समबाहु त्रिभुज है जिसकी भुजा 10 सेमी है।
इस प्रिज्म की ऊंचाई 10 \(√{3}\) सेमी है
प्रयुक्त अवधारणा:
प्रिज्म का टीएसए = [2(त्रिकोणीय आधार का क्षेत्रफल)] + [(आधार परिधि × ऊंचाई)]
समबाहु त्रिभुज का क्षेत्रफल = (√3/4)a2
समबाहु त्रिभुज का परिमाप = 3 × भुजा.
गणना:
अवधारणा के अनुसार,
⇒ समबाहु त्रिभुज का क्षेत्रफल = (√3/4)(10) 2 = (100/4)√3 = 25 √ 3
⇒ आधार परिमाप = 10 × 3 = 30
तब,
TSA = [2(25√3)] + [30 × 10√3]
⇒ TSA = 50√3 + 300√3
⇒ TSA = 350√3
∴ प्रिज्म का कुल सतह क्षेत्रफल 350 √ 3 है।
Last updated on Jun 13, 2025
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