Question

In the given figure, ABCD is a rectangle of dimensions 21 cm × 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure.

Answer 1

Area of the shaded region = Area of the rectangle − Area of the semicircle

`= 21 xx 14 - {1/2xx pi xx(14/2)^2}`

`=294 - {1/2 xx 22/7 xx 7 xx 7}`

= 294 - 77

`= 217 cm^2`

Therefore, area of shaded region is `217 cm^2`.

Length of the boundary (or perimeter) of the shaded region

= AB + AD + DC + arc BC

`= AB + AD + DC + 1/2 xx  2pi (14/2)`

`= 21 + 14 + 21 + 22/7 xx 7`

= 56 + 22

= 78 cm

Therefore, the perimeter of the shaded region is 78 cm.