Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

Solution:

14 cm = Side of the square ABCD (as given)

As a result, the area of ABCD = a²

= 14×14 cm² = 196 cm²

We know that the side of the square is also the diameter of the circle which = 14 cm

As a result, the side of the square = diameter of the semicircle which = 14 cm

Therefore, the radius of semicircle = 7 cm

Now, area of the semicircle = (πR²)/2

= (22/7×7×7)/2 cm² 

= 77 cm²

Therefore, the area of given two semicircles = 2×77 cm² = 154 cm²

Hence, area of the square – area of two semicircles = area of the shaded region

= 196 cm² -154 cm²

= 42 cm²