Let ABCD be a parallelogram. The lengths of the side AD and the diagonal AC are 10 cm and 20 cm, respectively. If the angle ∠ADC is equal to 30° then the area of the parallelogram is sq. cm. is
Explanation:
Let AE be a perpendicular from A to DC.
∆ADE is a 30-60-90 triangle. ⇒ DE = √3/2 × 10 = 5√3 ⇒ AE = 10/2 = 5
∆ACE is a right triangle. ⇒ CE2 = AC2 – AE2 ⇒ CE2 = 400 – 25 = 375 ⇒ CE = 5√15
∴ Area of parallelogram = 2 × Area of triangle ADC ⇒ Area of parallelogram = 2 × (1/2 × CD × AE) = CD × AE = (DE + EC) × AE = (5√3 + 5√15) × 5 = 25(√3 + √15)
Hence, option (c).
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