Question

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

(a) $256c{m}^2$

(b) $128c{m}^2$

(c) $64c{m}^2$

(d) $96c{m}^2$

Answer 1

ANSWER:
(b)$128c{m}^2$
ar(quad ABCD) = ar (∆ ABD) + ​ ar (∆ DBC)
We have the following:
ar(∆ ABD) = 1/2 × base ​ × height ​ = ​ 1/2× 16 ​ × 9 = $72c{m}^2$
ar(∆ DBC) = 1/2 × base ​ × height ​ = ​ 1/2 × 16 ​ × 7 = $56c{m}^2$
∴ ar(quad ABCD) =​ 72 + 56 = $128c{m}^2$