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

According to the given details , AC = 6cm  , BC = 8 cm

A triangle in a semi-circle with hypotenuse as diameter is right angled triangle.

On applying Pythagoras theorem in right angled triangle ACB,

(AB)² = (AC)² + (CB)²

∴  (AB)² = (6)² + (8)²

⇒(AB)² = 36 + 64

⇒(AB)² = 100 ⇒(AB)= 10

∴ Diameter of the circle = 10 cm

Thus, Radius of the circle = 5 cm

Area of circle = πr²

= π(5)²

= 25π cm²

= 25 × 3.14 cm²

= 78.5 cm²

We know that,

Area of the right angled triangle = ( ½ ) × Base × Height

= (½) × AC × CB

= (½) × 6 × 8

= 24 cm²

Now, Area of the shaded region = Area of the circle – Area of the triangle

= (78.5-24)cm²

= 54.5cm²