Question

In the figure given, PR = 22 cm, SN = MQ = 3 cm. What is the area of PQRS?

• A. 66 $c{m}^2$
• B. 63 $c{m}^2$
• C. 34 $c{m}^2$
• D. 198 $c{m}^2$

Answer 1

The correct option is A

66 $c{m}^2$

In the given figure, PR = 22 cm and SN = MQ = 3 cm.
The given rectangle can be considered as the combination of two triangles i.e. $△PSR$ and $△PQR$.
Now , area of rectangle PQRS = Area of $△PSR$ + Area of $△PQR$
Area of $△PSR$ = $\frac{1}{2}\times SN\times PR$
= $\frac{1}{2}\times 3\times 22$ = 3 $\times$ 11 = 33 $c{m}^2$

Area of $△PQR$ = $\frac{1}{2}\times QM\times PR$
= $\frac{1}{2}\times 3\times 22$ = 3 $\times$ 11 = 33 $c{m}^2$
$\Rightarrow$ Area of the rectangle = 33 $c{m}^2$ + 33 $c{m}^2$
= 66 $c{m}^2$
Therefore, area of the given figure is 66 cm${}^2$.