Question

Parallelogram PQRS, $\Delta \text{PQS}$ and rectangle PQTU have the same base PQ. If the area of $\Delta \text{PQS}=48c{m}^2$, then find the area of rectangle PQTU.

• A. $96{\text{cm}}^2$
• B. $48{\text{cm}}^2$
• C. $100{\text{cm}}^2$
• D. $50{\text{cm}}^2$

Answer 1

The correct option is A $96{\text{cm}}^2$


We know that diagonal divides the paralleogram into two triangles of equal areas.
In parallelogram PQRS,
$ar\Delta \text{PQS}=ar\Delta \text{QRS}=48c{m}^2$
$\Rightarrow \text{Area of Parallelogram PQRS = 2x48}$
$=96{\text{cm}}^2$

All rectangles are parallelograms.
Therefore, rectangle PQTU is a parallelogram.
Parallelograms on same base/equal bases and between same parallels are equal in area.
Therefore, area of parallelogram PQRS is equal to area of PQTU that is 96 ${\text{cm}}^2$.