# In Fig. 3, APB and AQO are semicircles, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region. Use π =227

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so for this figure, there are 2 semicircles APB and AQO

as AO=OB=r( given)

Perimeter of shaded region = circumference of semicircle APB + circumference of semicircle AQO

40 = r +r/2

80 = 3 r

r= 80/3 ...........1

Now Area of shaded region = r^2 + (r/2)^2 = (5 r^2)/4

Putting value of r from 1

we get area of shaded region as 283.09cm^2