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. 60 $c{m}^2$
• D. 46 $c{m}^2$

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 $△$ = $\frac{1}{2}\times height\times base$

Area of $△PSR$ $=\frac{1}{2}\times SN\times PR$
$=\frac{1}{2}\times 3\times 22=3\times 11=33c{m}^2$

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