In the given figure, find the area of the shaded region,

Question:

In the given figure, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are
semicircles.

 

Solution:

Area of the shaded region = Area of Square ABCD − (Area of semicircle APD + Area of semicircle BPC)

$=(14)^{2}-\left[\frac{1}{2} \pi\left(\frac{14}{2}\right)^{2}+\frac{1}{2} \pi\left(\frac{14}{2}\right)^{2}\right]$

$=(14)^{2}-\frac{22}{7}(7)^{2}$

 

$=42 \mathrm{~cm}^{2}$

Hence, the area of the shaded region is 42 cm2.

 

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