Question

ABCD is a diameter of a circle of radius 6cm .The lengths AB,BC,CD are equal . semicircles are drawn on AB and BD as diameter as shown in the given figure . Find the area of shaded region ​

Answer 1

Since, Length of AB, BC and CD are equal.

Radius of circle = 6 cm

Now, AD = 2 × 6 = 12 cm

⇒ AB + BC + CD = 12

⇒3AB = 12

⇒ \: AB \: = \: \frac{12}{3}⇒AB=

3

12

⇒AB=4cm

⇒AB=BC=CD=4cm

Radius of semicircle AB=2cm

Radius of semicircle BC=4cm

Radius of semicircle AD=6cm

Area of the shaded region = Area of semicircle (AB+AD) − Area of semicircle (BD)

⇒ Area \: of \: shaded \: region = \: 0.5\pi( {2}^{2} + {6}^{2}) \: - 0.5\pi {(4)}^{2}⇒ Areaofshadedregion =0.5π(2

2

+6

2

)−0.5π(4)

2

⇒ Area \: of \: shaded \: region = \: 0.6\pi(4 + 36) - 0.5\pi \times 16⇒ Areaofshadedregion =0.6π(4+36)−0.5π×16

⇒ Area \: of \: shaded \: region = \: 20\pi - 8\pi⇒ Areaofshadedregion =20π−8π

⇒ Area \: of \: shaded \: region = 12\pi {cm}^{2}⇒ Areaofshadedregion =12πcm

2