Question

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
as shown in the figure. Find the perimeter and area of the
shaded region.

Answer correctly.​

Answer 1

Step-by-step explanation:

ANSWER

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

So, AB=BC=CD=

3

12

=4cm

BD=BC+CD=4+4=8cm

Hence required perimeter=arc of semicircle of radius 6cm+ arc of semicircle of radius 4cm+ arc of semicircle of radius 2cm

=(π×6+π×4+π×2)cm

=12πcm.

Required Area = area of semicircle with AD as diameter+area of semicircle with AB as diameter−area of semicircle with BD as diameter.

=

2

1

×

7

22

×6

2

+

2

1

×

7

22

×2

2

−

2

1

×

7

22

×4

2

=

2

1

×

7

22

(6

2

+2

2

−4

2

)

=

7

264

cm

2

=37.71cm

2