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Question
In ΔABC, AB = 8cm, AC = 10cm and ∠B = 90°. P and Q are the points on the sides AB and AC respectively such that PQ = 3cm ad ∠PQA = 90. Find: Area of quadrilateral PBCQ: area of ΔABC.
Solution
In ΔAQP and ΔABC
∠A = ∠A
∠PQA = ∠ABC ...(right angles)
Therefore, ΔAQP ∼ ΔABC
Area(trapezium EDBC) = Area(ΔABC) - Area(ΔAQP)
Area(trapezium EDBC) = 24 - 6 = 18cm2
`("Area"("trapeziumEDBC"))/("Area"(Δ"ABC")) = (18)/(24)`
⇒ `("Area"("trapeziumEDBC"))/("Area"(Δ"ABC")) = (3)/(4)`
Area(trapezium EDBC): Area(ΔABC) = 3:4.
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