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# 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 - Mathematics

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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 pi=22/7]

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#### Solution

Let the radius of the semi-circle APB be r

⇒ The radius of the semi-circle AQO =r/2

Now,
Perimeter of the given figure = Length of arc AQO + Length of arc APB + OB

=pixxr/2+pixxr+r

=r(3/2pi+1)

=r(3/2xx22/7+1)

= r((33+7)/7)

=r(40/7)cm

r=7 cm

∴ Area of the shaded region = Area of semi-circle AQO + Area of semi-circle APB

=(pi(r/2)^2)/2+(pir^2)/2

=(pi(7/2)^2)/2+(pixx7^2)/2

=(49pi)/8+(49pi)/2

=49pi(1/8+1/2)

=49xx22/7xx5/8

= 96.25 cm2

Concept: Circumference of a Circle
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