Question

In the given figure, area of || gm ABCD is 80 cm². Find (i) ar(||gm ABEF) (ii) ar(∆ABD) and (iii) ar(∆BEF).

Answer 1

||​gm ABCD, ||gm ABEF, ∆ABD and ∆BEF lie on the same base and between the same parallel lines.

(i) ||gm ABCD and ||gm ABEF are on the same base and between the same parallels.
∴ ar(||gm ABEF) = ar(||​gm ABCD) = 80 cm²

(ii) ||​gm ABCD and ∆ABD lie on the same base and between the same parallels.
∴ ar(∆ABD) = $\frac{1}{2}$ ×​ ar (||gm ABCD) = $\frac{1}{2}$ ×​ 80 = 40 cm²

(iii) ||gm ABEF and ∆BEF lie on the same base and between the same parallel lines.
∴ ar(∆BEF) = $\frac{1}{2}$ ×​ ar (||gm ABEF) = $\frac{1}{2}$ ×​ 80 = 40 cm²​