Question

X and Y are the centers of $2$ circles on a square as shown in the figure. What is the area of the shaded portion? (Take $\pi =3.14$)

• A. $25.12c{m}^2$
• B. $28.26c{m}^2$
• C. $71.74c{m}^2$
• D. $88c{m}^2$

Answer 1

The correct option is C $71.74c{m}^2$

Each side of the square $=$ Diameter of the larger circle $+$ Radius of smaller circle

$=8cm+2cm=10cm$

$\therefore$ Area of shaded portion $=$ Area of the square $-$ Area of semicircle with centre Y $-$ Area of quarter circle with centre X

$=100-(\frac{1}{2}\times 3.14\times 16)$$-(\frac{1}{4}\times 3.14\times 4)$

$=100-25.12-3.14$

$=71.74c{m}^2$