Question

Calculate the area of the shaded region in the figure, where $\square ABCD$ is a square with side 8 cm each. $(\pi =3.14)$

• A. $36.48c{m}^2$
• B. $25.40c{m}^2$
• C. $15c{m}^2$
• D. $65c{m}^2$

Answer 1

The correct option is A $36.48c{m}^2$

Area of square =$Sid{e}^2$
=$8^2$
=$64$ sq cm
Area of shaded portion = Double area of segment formed by diagonal of the square
Area of two quadrants =$\frac{1}{2}\pi r^2$

=$\frac{1}{2}\times 3.14\times 8^2$

=$100.48$ sq cm
Area of square - Area of two triangles formed by radii and the cord
So,
Area of shaded portion =$100.48-64$
=$36.48sq$ cm