Question
Download Solution PDFदी गयी आकृति में, PQRS एक चतुर्भुज है। यदि QR = 18 सेंटीमीटर और PS = 9 सेंटीमीटर, तो चतुर्भुज PQRS का क्षेत्रफल (वर्ग सेंटीमीटर) में क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFरेखा QP और RS को बढ़ाएं जो वे T पर मिलेंगी और वे एक समबाहु त्रिभुज बनाएंगी
∆QRT एक समबाहु त्रिभुज है, भुजा = 18 सेंटीमीटर,
⇒ ∆QRT का क्षेत्रफल = √3/4 × 18 × 18 = 81√3 वर्ग सेंटीमीटर
⇒ ∆TSP समकोण त्रिभुज है, PS = 9 सेंटीमीटर,
⇒ TS = 9 tan 30° = 9/√3 सेंटीमीटर
⇒ ∆TSP का क्षेत्रफल = 1/2 × 9/√3 × 9 = (27√3)/2 वर्ग सेंटीमीटर
अब चतुर्भुज PQRS का क्षेत्रफल = ∆QRT का क्षेत्रफल - ∆TSP का क्षेत्रफल
⇒ चतुर्भुज PQRS का क्षेत्रफल = [81√3 - (27√3)/2]
∴ चतुर्भुज PQRS का क्षेत्रफल = (135√3)/2 वर्ग सेंटीमीटर
Last updated on Jul 21, 2025
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