Question

In the given figure, ABCD and PQRS are two parallelograms. If AP = BQ, then which of the following is true?

• A.
  $ar\left(PQRS\right)=ar\left(ABCD\right)$
• B.
  $ar\left(PQRS\right)=\frac{1}{4}ar\left(ABCD\right)$
  
• C.
  $ar\left(PQRS\right)=\frac{1}{2}ar\left(ABCD\right)$
  
• D.
  $3ar\left(PQRS\right)=ar\left(ABCD\right)$
  

Answer 1

The correct option is A

$ar\left(PQRS\right)=ar\left(ABCD\right)$
Let the height of the given two parallelograms ABCD and PQRS be h.

Given that AP = BQ.

Now, adding PB to both the sides, we get



$AP+PB=PB+BQ\Rightarrow AB=PQ$

We know that parallelogram on the same base and between the same parallels are equal in area.
ABCD and PQRS lie on the same base AB = PQ and between the same parallels AQ and SC.

$\therefore Ar\left(ABCD\right)=Ar\left(PQRS\right)$

Hence, the correct answer is option (a).