Question
Download Solution PDFIn trapezium ABCD, ∠BAE = 30°, ∠CDF = 45°, BC = 6 cm and AB = 12 cm. Find the area of ABCD.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFIn ΔABE,
⇒ cos30° = AE/AB
⇒ AE = 6√3 cm
⇒ sin30° = BE/AB
⇒ BE = 6 cm
In ΔCFD,
⇒ tan45° = CF/FD
⇒ FD = 6 cm [∵ BE = CF = 6cm]
⇒ AD = AE + EF + FD
⇒ AD = 6√3 + 6 + 6 cm
⇒ AD = 12 + 6√3 cm
⇒ Area of trapezium = 1/2 × (sum of parallel sides) × height
⇒ Area of trapezium = 1/2 × (BC + AD) × BE
∴ Area of trapezium = 1/2 × (12 + 6√3 + 6) × 6 = 18(3 + √3) cm2
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