In a quadrilateral ABCD, it is given that BD = 16cm. If AL ⊥ BD and CM ⊥ BD such that AL = 9cm and CM = 7cm, then ar(quad.ABCD) = ?

Question

Philoid · Accepted Answer

Given:

BD = 16cm

AL ⊥ BD

CM ⊥ BD

AL = 9cm

CM = 7cm

Here,

Area of quadrilateral ABCD = area(ΔABD) + area(ΔBCD)

Area of triangle = 1/2 × base × height

area(ΔABD) = 1/2 × base × height = 1/2 × BD × CM = 1/2 × 16 × 7 = 56cm²

area(ΔBCD) = 1/2 × base × height = 1/2 × BD × AL = 1/2 × 16 × 9 = 64cm²

∴ Area of quadrilateral ABCD = area(ΔABD) + area(ΔBCD) = 56 + 64 = 120cm²