Question

In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.  [Use Π = 22/7]

Answer 1

Radius (r₁) of larger circle = 7 cm

Radius (r₂) of smaller circle = 7/2 cm

Area of smaller circle = `pir_1^2`

`=22/7xx7/2xx7/2`

`= 77/2 cm^2`

Area of semi-circle AECFB of larger circle  = `1/2 pir_2^2`

`=1/2xx22/7xx(7)^2`

= 77 cm²

Area of ΔABC = `1/2 xx AB xx OC`

`= 1/2xx14xx7 = 49 cm^2`

Area of the shaded region

= Area of smaller circle + Area of semi-circle AECFB − Area of ΔABC

`= 77/2 + 77 - 49`

`= 28+77/2 = 28 + 38.5 = 66.5 cm^2`