Question

In figure, AB is a diameter of the circle, AC = 6 cm and BC = 8 cm. Find the area of the shaded region (Use π = 3.14).

Answer 1

Given, AC = 6 cm and BC = 8 cm

We know that, triangle in a semi-circle with hypotenuse as diameter is right angled triangle.

∴ ∠C = 90°

In right angled ΔACB, use Pythagoras theorem,

∴ AB² = AC² + CB²

⇒ AB² = 6² + 8²

⇒ AB² = 36 + 64

⇒ AB² = 100

⇒ AB = 10 cm   ...[Since, side cannot be negative]

∴ Area of ΔABC = ${\displaystyle \frac{1}{2}\times \text{BC}\times \text{AC}}$

= ${\displaystyle \frac{1}{2}\times 8\times 6}$

= 24 cm²

Here, diameter of circle,

AB = 10 cm

∴ Radius of circle,

r = ${\displaystyle \frac{10}{2}}$ = 5 cm

Area of circle = πr²

= 3.14 × (5)²

= 3.14 × 25

= 78.5 cm²

∴ Area of the shaded region = Area of circle – Area of ΔABC 

= 78.5 – 24

= 54.5 cm²