Question

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.
​

Answer 1

Answer:

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=

3

12

⇒ AB= 4cm

⇒ AB= BC= CD= 4cm

Radius of semicircle AB

=

2

cm

Radius of semicircle BC

=

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(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