Question

Find the area of shaded region in the given fig. where ABCD is a square of side 10cm and semi-circles are drawn with each side of square as diameter. [$\pi =3.14$]

• A. $57c{m}^2$
• B. $56c{m}^2$
• C. $108c{m}^2$
• D. $48c{m}^2$

Answer 1

The correct option is A

$57c{m}^2$

Area of region I + III = area of ABCD - area of two semicircles of each radius 5cm

$=10\times 10-2\times 0.5\times \frac{22}{7}\times 5^2$

$=21.5c{m}^2$

Similarly area of II + area IV $=21.5c{m}^2$

Area of region I, II, III, and IV $=2\times 21.5=43c{m}^2$

Thus area of shaded region = Area ABCD - Area of (I, II, III, IV)

$=100-43=57c{m}^2$