In the adjoining figure, ABCD is a quadrilateral in which diagonal BD = 14cm. If AL ⊥ BD and CM ⊥ BD such that AL = 8 cm and CM = 6 cm, find the area of quad. ABCD.

Question

Philoid · Accepted Answer

Given: BD = 14cm, AL = 8 cm, CM = 6 cm and also, AL ⊥ BD and CM ⊥ BD.

Here,

Area (Quad.ABCD) = Area (ΔABD) + Area (ΔABC)

Area (ΔABD) = 1/2 base × height = 1/2 × BD×AL = 1/2 × 14 × 8 = 56cm²

Area (ΔABC) = 1/2 base × height = 1/2 × BD×CM = 1/2 × 14 × 6 = 42cm²

∴ Area (Quad.ABCD) = Area (ΔABD) + Area (ΔABC) = 56 + 42 = 98 cm²

∴ Area (Quad.ABCD) = 98 cm²