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. (Use $\pi =3.14$)

Answer 1

Here, AC = 24 cm and BC = 10 cm and AOB is a diameter.
Since, angle in semicirle is a right angle, i.e., Angle ACB = 900
AB = Root AC^2 + BC^2
= Root 24^2 + 10^2
= Root 576 + 100
= Root 676 = 26 cm.
Therefore, Radius of circle = 13 cm.

Now, area of the shaded region
= Area of semicircle - Area of triangle ABC
= 1/2 pie*r^2 - 1 /2 * BC * AC

= 1/2 * 3.14 * 13 * 13 - 1/2 * 24 * 10

= 530.66 /2- 120


= 265.33 - 120

= 145.33 cm^2 .
Hope this helps.