Question

In the given figure, if ABCD is a parallelogram of area 90 cm². Then, ar(||^gm ABEF) = ________ ar(ΔABD) = _______ and ar(ΔBEF) = _________.

Answer 1

Given:
ABCD is a parallelogram of area 90 cm²


ABCD and ABEF are two parallelograms lying on the same base AB and between the same parallels AB and CF.

We know, if two parallelograms are on the same base and between the same parallels, then the area of the parallelograms are equal.

Thus, ar(ABCD) = ar(ABEF) = 90 cm² ...(1)

Also, ΔABD and parallelogram ABEF is lying on the same base AB and between the same parallels AF and BE.

We know, if a triangle and a parallelogram are on the same base and between the same parallels, then the area of the triangle is half the area of the parallelogram.

Thus, ar(ΔABD) = $\frac{1}{2}$ar(ABEF)
⇒ ar(||^gm ABEF) = 2 ar(ΔABD) ...(2)

From (1) and (2),
ar(||^gm ABEF) = 2 ar(ΔABD) = 90 cm²
​
Also, diagonal of a parallelogram divides it into two triangles of equal area.
Thus, ar(ΔBEF) = $\frac{1}{2}$ar(ABEF)
= $\frac{1}{2}$(90)
= 45 cm²


Hence, ar(||^gm ABEF) = 2 ar(ΔABD) = 90 cm² and ar(ΔBEF) = 45 cm².