Question

AD is the diameter of a circle of radius 6cm and AB = BC = CD. Semi-circles are draw with AB and BD as diameters as shown in the figure. Find the Perimeter and Area of the shaded region. ​

Answer 1

Answer:

Perimeter = 12 πcm and Area = 37.71cm²

Step-by-step explanation:

We have AD = diameter of circle of radius 6cm

So, AB = BC = CD = 12/3 = 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

= 12 πcm.

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 x 22/7 x 6²+1/2 x 22/7 x 2² - 1/2 x 22/7 x 4²

=  1/2 x 22/7 ( 6²+2²- 4²)

= 264/7 cm²

= 37.71cm²

 

    I hope this answer will help you...................