Q16 of 47 Page 1

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

Let the radius of bigger semicircle, APB be R.

OA = OB = R
Diameter of smaller semicircle, AQO = Radius of the bigger semicircle, APB


Therefore, Radius of smaller semicircle, AQO = R/2


Perimeter of the figure = Circumference of APB + BO + Circumference of OQA


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⇒ R = 7cm


Area of the shaded region = Area of bigger semicircle + Area of smaller semicircle


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⇒ ⇒ cm2


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