Question

Find the area of the unshaded region in Fig, where ABCD is a square of side 20 cm and semicircles are drawn with each side of the square as diameter. (Use π = 3.14)​

Answer 1

229

Explanation:

Area of square is = 20 * 20 = 400

radius = 20 / 2 = 10

Area of semi circle is = 1/2 * πr²

= 1/2 * 3.14 * 10²

= 1/2 / 314

= 157

assume there are four shaded regions for the figure

Area of 4 semicircles−Area of shaded region=Area of square ABCD

Area of shaded region=Area of 4 semicircles−Area of square ABCD

= 4 * 157 - 400

= 628 - 400

= 228

so each single shaded area is 228/4

= 57

now in your problem there are 3 shaded regions like this

so area of unshaded region is =

Area of square - 3 * shaded region area of one region

=> 400 - 3 * 57

=> 400 - 171

=> 229