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.
​

Answer 1

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Answer:

12πcm^2

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Asked on December 26, 2019 by

Mishal Castelino

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

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ANSWER

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=

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 =0.5π(2

2

+6

2

)−0.5π(4)

2

⇒ Area of shaded region =0.6π(4+36)−0.5π×16

⇒ Area of shaded region =20π−8π

⇒ Area of shaded region =12πcm^2

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