Question
Download Solution PDFएक समलंब चतुर्भुज की समांतर भुजाएँ 48 सेमी और 20 सेमी हैं। इसकी असमांतर भुजाएँ 26 सेमी और 30 सेमी हैं। समलंब चतुर्भुज का क्षेत्रफल (सेमी² में) क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
समांतर भुजाएँ: a = 48 सेमी, b = 20 सेमी
असमांतर भुजाएँ: c = 26 सेमी, d = 30 सेमी
प्रयुक्त सूत्र:
समलंब चतुर्भुज का क्षेत्रफल = ½ × (a + b) × ऊँचाई (h)
ऊँचाई (h) ज्ञात करने के लिए: h = √(c² - m²), जहाँ m = ((a - b)² + c² - d²) / (2 × (a - b))
गणनाएँ:
a - b = 48 - 20 = 28
m = [28² + 26² - 30²] / (2 x 28)
m = (784 + 676 - 900) / 56 = (560) / 56 = 10
h = √(26² - 10²) = √(676 - 100) = √576 = 24 सेमी
क्षेत्रफल = ½ × (48 + 20) × 24 = ½ × 68 × 24 = 34 × 24 = 816 सेमी²
∴ समलंब चतुर्भुज का क्षेत्रफल = 816 सेमी²
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