Question

4. ABCD is a diameter of a circle
of radius 6 cm such that
AB = BC = CD. Semicircles a
DUB ČD
are drawn on AB and BD
as diameters, as shown in
the adjoining figure. Find the area
of the shaded region.​

Answer 1

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Area of shaded region = 12π cm²

step of explanation:

Length of AB, BC and CD are equal

Radius of circle = 6 cm

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

Answer 2

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