Question

If the given figure, PQRS and EFRS are two parallelograms, then ar(||^gm PQRS) : ar(ΔMFR) = ________.

Answer 1

Given:
PQRS and EFRS are two parallelograms



PQRS and EFRS are two parallelograms lying on the same base SR and between the same parallels SR and PF.

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(PQRS) = ar(EFRS) ...(1)

Also, ΔMFR and parallelogram EFRS is lying on the same base FR and between the same parallels SR and EF.

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(ΔMFR) = $\frac{1}{2}$ar(EFRS) ...(2)

From (1) and (2),
ar(ΔMFR) = $\frac{1}{2}$ar(PQRS)
⇒ ar(||^gm PQRS) = 2 ar(ΔMFR)
​

Hence, ar(||^gm PQRS) : ar(ΔMFR) = 2 : 1.