Question

in the figure, AC = 24 cm, BC=10cm and o is the centre of the circle . find the area of shaded region.(π =3.14)

Answer 1

Finding the diameter of the circle at first:

AC=24cm, BC= 10 cm

So, AB= √AC²+BC² = √576+100 = √676 = 26cm

Therefore, the diameter of the circle is 26cm.

So,the radius is 13cm(r).

Now,finding the area of the semi-circle AOBC:

Area of semi-circle, A=(πr^2)/2 = 265.33 cm²

Now,finding the area of the right-angled triangle,ABC:

Area= ½ * base *height = 120cm²

Therefore, area of the shaded portion= Area of semi-circle AOBC - Area of triangle ABC= 265.33-120cm²= 145.33cm²

Ans: 145.33 cm²

Answer 2

According Pythogora’s theorem,

AB2= AC2 + BC2

= 24.24 + 10.10

= 576 + 100

= 676 cm2

Therefore, AB= 26 cm

Therefore radius of the circle = 26/2= 13 cm

Area of the shaded portion

= area of the semi circle – area of the triangle

=  ½ pie r2 – ½ base* height

= ½ * 3.14 * 13* 13 – ½ *10* 24

= 145.33 cm square