In the given figure, the area of ||gm ABCD is 90 cm². State giving reasons:

(i) ar (||gm ABEF)

(ii) ar (△ABD)

(iii) ar (△BEF)

(i) ar (||gm ABEF)

||gm ABCD and ||gm ABEF lie on the same base AB and between the same parallels AB and FC.

∴ ar(||gm ABEF) = ar(||gm ABCD) = 90 cm².

Hence, ar(||gm ABEF) = 90 cm².

(ii) Triangle ABD and parallelogram ABCD are on the same base AB and between the same parallels AB and CD, then area of triangle is equal to half of the area of the parallelogram.

ar (△ABD) = $\dfrac{1}{2}$ ar(||gm ABCD)

= $\dfrac{1}{2} \times 90$

= 45 cm².

Hence, ar (△ABD) = 45 cm².

(iii) Triangle BEF and a parallelogram ABEF are on the same base EF and between the same parallels AB and EF, then area of triangle is equal to half of the area of the parallelogram.

ar (△BEF) = $\dfrac{1}{2}$ ar(||gm ABEF)

= $\dfrac{1}{2} \times 90$

= 45 cm².

Hence, ar (△BEF) = 45 cm².