Question

In the given figure ABC is a right angled triangle at A. semicircle are drawn on AB,AC and BC as diameter.find the area of shaded region

Answer 1

BC²=AC²+AB²

=8²+6²

=64+36

=100

BC=10cm

Area of biggest semicircle= 1/2 * 3.14 * r² =0.5*3.14*5*5

=0.5*78.5

=39.25 cm²

Area of 2nd Largest Semicircle = 0.5*3.14*r² =0.5*3.14*3² =0.5*3.14*9 =14.13 cm²

Area of smallest Semicircle = 0.5*3.14*r² =0.5*3.14*4² =0.5*3.14*16 =25.12 cm²

Area of Triangle = 1/2 *b*h

= 0.5*6*8

=24 cm²

Area of shaded region = (24+25.12+14.13) - 39.25

= 63.25-39.25

=24 cm²