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.

Answer 1

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.