Question

In the figure, $ABCD$ is a square of side $14$ cm and $A,B,C,D$ are centres of arcs, each of radius $7$ cm. Find the area of the shaded region.

• A. $42$ sq. cm
• B. $402$ sq. cm
• C. $44$ sq. cm
• D. $48$ sq. cm

Answer 1

The correct option is A $42$ sq. cm

Area of square $={\text{Side}}^2={14}^2=196$ sq. cm
Area of four quadrants is equal to area of $1$ circle.
Therefore, area of circle $=\pi r^2$ $=\frac{22}{7}\times 7^2$
$=154$ sq cm
Thus area of shaded portion $=196-154=42$ sq. cm