Find the area of a square

Problem:
Find the area of the shaded design in below fig where ABCD is a square of side 10 cm a semicircles are drawn with each side of the square as diameter. (Use π = 3.14).


Solution : Let us mark the four unshaded regions as I, II, III and IV .Area of I + Area of III = Area of ABCD – Areas of two semicircles of each of radius 5 cm
(10×10-2×1/2×π×52)cm2= (100 – 3.14 × 25) cm2
= (100 – 78.5) cm2 = 21.5 cm2
Similarly, Area of II + Area of IV = 21.5 cm2
So, area of the shaded design = Area of ABCD – Area of (I + II + III + IV)
= (100 – 2 × 21.5) cm2 = (100 – 43) cm2 = 57 cm2