Question

с
B
D
А
10. ABCD is a diameter of a circle of radius 6 cm. The lengths AB,
BC and CD are equal. Semicircles are drawn on AB and BD as
diameters as shown in the given figure. Find the area of the shaded
region. (Take a = 3.14)​

Answer 1

Since, length of AB, BC and CD are equal

Radius of circle = 6cm

Now, AD = 2 × 6 = 12cm

⇒ AB + BC + CD = 12

⇒ 3AB = 12

⇒ AB = 12/3

⇒ 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 = $\sf{0.5\pi( {2}^{2} + {6}^{2}) - 0.5\pi( {4}^{2})}$

⇒ Area of shaded region = $\sf{0.6\pi(4 + 36) - 0.5\pi \times 16}$

⇒ Area of shaded region = $\sf{20\pi-8\pi}$

⇒ Area of shaded region = $\sf{12\pi {cm}^{2}}$