Question

A right angled triangle of sides containing right angle are 6 cm and 8 cm is
circumscribed in a circle with centre o of radius 5 cm as shown in the
figure. Find the area of the shaded region.​

Answer 1

Given:

A right angled triangle with sides 6 cm and 8 cm

Radius of circle = 5 cm

To Find:

Area of the shaded region

Formula:

$\text{Area of a circle} = \pi r^2$

$\text{Area of a triangle} = \dfrac{1}{2} \times \text{base} \times \text{height}$

Find the area of the circle:

$\text{Area of a circle} = \pi r^2$

$\text{Area of the circle} = \pi (5)^2$

$\text{Area of the circle} = 25 \pi \text{ cm}^2$

Find the area of the triangle:

$\text{Area of a triangle} = \dfrac{1}{2} \times \text{base} \times \text{height}$

$\text{Area of the triangle} = \dfrac{1}{2} \times \text{6} \times \text{8}$

$\text{Area of the triangle} = 24 \text{ cm}^2$

Find the area of the shaded region:

$\text{Shaded Region } = 25\pi -24$

$\text{Shaded Region } = 54.57 \text{ cm}^2$

Answer: The shaded region is 54.57 cm²