Sum

In the given figure, APB and AQO are semicircles and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region.

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#### Solution

Permieter of shaded region = Length of the arc AQO + Length of the arc APB + Length of OB

`=>40=1/2xx2pi("AO"/2) + 1/2xx2pi("OB") +"OB"`

`= 40 = 11/7"AO"+22/7"OB"+"OB"`

`=40 = 11/7"OB "+ 22/7 "OB" + "OB"` [∴ AO = OB]

`=> 40 = 40/7 "OB"`

⇒ OB =7 cm

Area of the shaded portion = Area of semicircle AQO + Area of semicircle APB

`=1/2 pi(7/2)^2 + 1/2(7)^2`

`= 1/2 xx 22/7xx(7/2)^2+1/2xx22/7xx(7)^2`

= 96.25 cm^{2 }

Hence, the area of the shaded portion is 96.25 cm^{2}.

Concept: Circumference of a Circle

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