Question
Download Solution PDFसमलम्ब चतुर्भुज ABCD में, ∠BAE = 30°, ∠CDF = 45°, BC = 6 सेमी. और AB = 12 सेमी. हो, तो ABCD का क्षेत्रफल ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFΔABE में,
⇒ cos30° = AE/AB
⇒ AE = 6√3 सेमी.
⇒ sin30° = BE/AB
⇒ BE = 6 cm
ΔCFD में,
⇒ tan45° = CF/FD
⇒ FD = 6 सेमी. [∵ BE = CF = 6 सेमी.]
⇒ AD = AE + EF + FD
⇒ AD = 6√3 + 6 + 6 सेमी
⇒ AD = 12 + 6√3 सेमी
⇒ समलम्ब चतुर्भुज का क्षेत्रफल = 1/2 × (समानांतर भुजाओं का योग) × ऊंचाई
⇒ समलम्ब चतुर्भुज का क्षेत्रफल = 1/2 × (BC + AD) × BE
∴ समलम्ब चतुर्भुज का क्षेत्रफल = 1/2 × (12 + 6√3 + 6) × 6 = 18(3 + √3) वर्ग सेमी.Last updated on Jun 13, 2025
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