Question

Find the area of the shaded region in Fig., if AC = 24 cm, BC = 10 cm and O is the center of the circle.

Answer 1

Given,

AC = 24 cm and BC = 10 cm

Since, AB is the diameter of the circle

Angle ACB = 90^o

So, using Pythagoras theorem

AB² = AC² + BC² 

= 24² + 10² 

= 576 + 100 

= 676

AB = √676 = 26 cm

Thus, the radius of the circle = 26/2 

= 13 cm

The area of shaded region = Area of semi-circle – Area of triangle ACB

= 1/2 πr² – 1/2 x b x h

= 1/2 (22/7)13² – 1/2 x 10 x 24

= 265.33 – 120

= 145.33 cm²