In the adjoining figure, ABC is a right angled triangle at B. A semicircle is drawn on AB as diameter. If AB = 12 cm and BC = 5 cm, then the area of the shaded region is

1. (60 + 18π) cm²

2. (30 + 36π) cm²

3. (30 + 18π) cm²

4. (30 + 9π) cm²

Area of right angle triangle ABC = $\dfrac{1}{2}$ × base × height

= $\dfrac{1}{2}$ × AB × BC

= $\dfrac{1}{2}$ × 12 × 5

= 30 cm².

From figure,

AB = 12 cm is the diameter of circle.

Radius = $\dfrac{AB}{2}$ = 6 cm.

Area of semi-circle = $\dfrac{πr^2}{2} = \dfrac{π(6)^2}{2} = \dfrac{36π}{2}$ = 18π cm².

Area of shaded region = Area of right angle triangle ABC + Area of semi-circle

= (30 + 18π) cm².

Hence, Option 3 is the correct option.