Question

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.
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Answer 1

Answer:

Area of shaded region = 12π cm²

Step-by-step explanation:

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 = 4 cm

⇒ AB = BC = CD = 4 cm

Radius of semicircle AB = 2 cm

Radius of semicircle BD = 4 cm

Radius of semicircle AD = 6 cm

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

⇒ Area of shaded region = 0.5π( 2² + 6² ) - 0.5π(4²)

⇒ Area of shaded region = 0.5π (4 + 36) - 0.5π × 16

⇒ Area of shaded region = 20π - 8π

⇒ Area of shaded region = 12π cm²