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In the figure given below, ABCD is the diameter of a circle of radius 9 cm. The lengths AB, BC and CD are equal. Semicircles are drawn on AB and BD as diameters as shown in the figure. What is the area of the shaded region?

In the figure given below, ABCD is the diameter of a circle of radius 9 cm. The lengths AB, BC and CD are equal. Semicircles are drawn on AB and BD as diameters as shown in the figure. What is the area of the shaded region? Correct Answer 27π

Diameter of circle = AD = 2(9) = 18 cm

⇒ AB = BC = CD = 18/3 = 6 cm

⇒ BD = BC + CD = 6 + 6 = 12 cm

∵ Area of semi-circle = (π/8) × (diameter)2

⇒ Area of semi-circle with diameter AD = (π/8) × (18)2 = 81π/2 cm2

⇒ Area of semi-circle with diameter AB = (π/8) × (6)2 = 9π/2 cm2

⇒ Area of semi-circle with diameter BD = (π/8) × (12)2 = 18π cm2

∴ Area of shaded region = (81π/2) + (9π/2) – 18π = 45π – 18π = 27π cm2

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