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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 - CBSE Class 10 - Mathematics

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Question

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`]

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

  Is there an error in this question or solution?
Solution 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 Concept: Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle.
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