Question

In the given figure, $P Q R S$ is a square of diagonal $7 \sqrt{2} \mathrm{~cm}$. With $P$ as centre and $P Q$ as radius, the arc $Q S$ is drawn. Find the area of the shaded region (in $\mathrm{cm}^2$ ).

• A. $\frac{21}{2}$
• B. 14
• C. 21
• D. 42

Answer 1

Answer: (A)

Diagonal of the square $=7 \sqrt{2} \mathrm{~cm}$
$\Rightarrow \text { Side }=\frac{7 \sqrt{2}}{\sqrt{2}}=7 \mathrm{~cm}$
(Area of the shaded region) = (Area of the square) - (Area of the sector PQS)
$=7^2-\frac{90^{\circ}}{360^{\circ}} \times \frac{22}{7} \times(7)^2=\frac{21}{2} cm ^2$