Question
In parallelogram ABCD, AB = 10 cm, BC = 7 cm and
diagonal AC = 13 cm. Find the area of the parallelogram.Solution
Let ∠ABC = θ. In triangle ABC: AC² = AB² + BC² − 2·AB·BC·cosθ 13² = 10² + 7² − 2×10×7×cosθ 169 = 100 + 49 − 140 cosθ 169 = 149 − 140 cosθ −140 cosθ = 169 − 149 = 20 cosθ = −20/140 = −1/7 Then sinθ = √(1 − cos²θ) = √(1 − 1/49) = √(48/49) = (4√3)/7 Area of parallelogram = AB × BC × sinθ = 10 × 7 × (4√3/7) = 40√3 cm².
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