Given figure,

It is given that PQRS and MONS are rectangles with M and N as the mid-point of PS and SR respectively. So,

$\begin{aligned} P M &=M S \\ &=\frac{1}{2} P S \\ S N &=R N \\ &=\frac{1}{2} S R \end{aligned}$

Now,

$\operatorname{ar}(M O N S) &=\ { base } \times \ { height } \\ &=S N \times M S \\ &=\frac{1}{2} S R \times \frac{1}{2} P S \\ &=\frac{1}{4} P S \times S R...............(1)$

Similarly,

$\operatorname{ar}(P Q R S)=P S \times S R .............(2)$

From equation (1) and (2),

$\begin{aligned} \operatorname{ar}(P Q R S) &=P S \times S R \\ &=4 \times \operatorname{ar}(M O N S) \end{aligned}$

Rectangle $M O N S and \Delta A N S$ lie on the same base and between the same parallel. So,

$\operatorname{ar}(M O N S)=2 \times \operatorname{ar}(\Delta A N S)$

Now,

$\begin{aligned} \operatorname{ar}(P Q R S) &=4 \times \operatorname{ar}(M O N S) \\ &=4 \times 2 \times \operatorname{ar}(\Delta A N S) \\ &=8 \times \operatorname{ar}(\Delta A N S) \\ \operatorname{ar}(\Delta A N S) &=\frac{1}{8} \operatorname{ar}(P Q R S) \end{aligned}$

Therefore, both option A and Bare correct.

SELF STUDY

Parallelogram on the Same Base

Quick practice

Question 1 of 5

Get unlimited practice with Dormant subscription