Question

In a quadrilateral ABCD, it is given that BD = 16 cm. If AL ⊥ BD and CM ⊥ BD such that AL = 9 cm and CM = 7 cm, then ar(quad. ABCD) = ?
(a) 256 cm²
(b) 128 cm²
(c) 64 cm²
(d) 96 cm²

Answer 1

(b)128 cm²

ar(quad ABCD) = ar (∆ ABD) + ​ar (∆ DBC)
​
We have the following:
ar(∆ABD) = $\frac{1}{2}$ × base ​× height ​= ​$\frac{1}{2}$× 16 ​× 9 = 72 cm²
ar(∆DBC) = $\frac{1}{2}$ × base ​× height ​= ​$\frac{1}{2}$ × 16 ​× 7 = 56 cm²

∴ ar(quad ABCD) =​ 72 + 56 = 128 cm²