Question

Find the area of the shaded region

• A. 62cm${}^2$
• B. 43cm${}^2$
• C. 57cm${}^2$
• D. 38cm${}^2$

Answer 1

The correct option is B 43cm${}^2$

Divide the square ABCD into equal four parts

and take one part which is given by

Area of shaded region in this part = Area of square DPOS - Area of the unshaded region
and area of PDMO = $5^2$ - $\frac{1}{4}\pi r^2$ = $25-\frac{1}{4}\times 3.14\times 25$ = 5.375cm${}^2$

Therefore area of the shaded region in square DPOS = $5.375\times 2$ = 10.75 cm${}^2$

As DPOS is a quarter of square ABCD,
Total area of the shaded region = $4\times 10.75$= 43cm${}^2$