Question

cm.
2. AD is the diameter of a circle of radius 6 cm and AB = BC
= CD. Semi-circles are drawn with AB and BD as diameters at
as shown in the figure. Find the perimeter and area of the
shaded region.

.​

Answer 1

Answer:

We have,

AD=diameter of circle of radius 6cm=12cm

Therefore,AB=BC=CD=

12

3

=

4

c

m

BD=BC+CD

=

(

4

+

4

)

c

m

=

8

c

m

Hence required perimeter

=

arc of semicircle of radius 6cm+ arc of circle of radius 4 cm+ arc of circle of radius 2cm

=

(

π

×

6

+

π

×

4

+

π

×

2

)

c

m

=

12

π

c

m

Required area

=

area of semicircle with AD as diameter

+

area of semicircle with AB as diameter

−

area of semicircle with BD as diameter

=

1

2

×

22

7

×

6

2

+

1

2

×

22

7

×

2

2

−

1

2

×

22

7

×

4

2

=

1

2

×

22

7

(

6

2

+

2

2

−

4

2

)

=

1

2

×

22

7

×

24

=

264

7

c

m

2

=

37.71

c

m

2