Question

In the given figure O is the centre of the circle AOB is the diameter, AC = 12 cm and BC = 16 cm. Find the area of the shaded region​

Answer 1

Answer:

Area of the shaded region :

$61 \: {cm}^{2}$

Step-by-step explanation:

Angle C = 90 degrees. ( angle in a semicircle since AB is the diameter)

=> (AB)^2 = (AC)^2 + (BC)^2

=> (AB)^2 = 144 + 256

=> (AB)^2 = 400

=> Diameter of the circle (AB) = 20 cm

=> radius = 10 cm

Area of triangle ABC

= 1/2 x base x height

= 1/2 x 12 x 16

= 96 cm^2

Area of semicircle AOBC

= 1/2 x πr^2

= 1/2 x 3.14 x 100

= 157 cm^2

Area of shaded region = Area of Semicircle AOBC - Area of triangle ABC

= 157 - 96

= 61 cm^2