Question

ABCD is a rectangle, having AB = 20 cm and BC = 14 cm. Two sectors of ${180}^{\circ }$ have been cut off. Calculate

(i) The area of the shaded region

(ii) The length of the boundary of the shaded region.

Answer 1

i) We have given two semi-circles and a rectangle.

Area of the shaded region = Area of the rectangle − Area of the two semicircles ……..(1)

$Areaoftheshadedregion=20\times 14-2\times \frac{1}{2}\times \pi \times 7^2$

Substituting $\pi =\frac{22}{7}$ we get,

$Areaoftheshadedregion=20\times 14-2\times \frac{1}{2}\times \frac{22}{7}\times 7^2$

$=20\times 14-22\times 7=280-154=126$

Therefore, area of shaded region is 126 cm²

(ii) Now we will find length of the boundary of the shaded region.

$Lengthoftheboundaryoftheshadedregion=2\pi r+AB+DC=2\times \frac{22}{7}\times 7+20+20$

$=2\times 22+40=44+40=84$

Therefore, length of the boundary of the shaded region is 84 cm.