Question

Find the area of shaded region if ACB is a right-angled triangle with AC = 8.66 cm, BC = 11 cm, and diameter AB = 14 cm.

• A. 29.37 $c{m}^2$
• B. 38.5 $c{m}^2$
• C. 47.63 $c{m}^2$
• D. 77 $c{m}^2$

Answer 1

The correct option is A 29.37 $c{m}^2$

Diameter = 2$\times$radius
radius = $\frac{diameter}{2}$ = $\frac{14}{2}$ = 7 cm
Area of shaded region =
Area of semicircle - Area of triangle ACB

Area of semicircle = $\frac{1}{2}$$\times$pi$\times$$r^2$
...... where r is radius of circle
=$\frac{1}{2}$$\times$$\frac{22}{7}$$\times$$7^2$ = $\frac{1}{2}$$\times$$\frac{22}{7}$$\times$$49$
= 11$\times$7= 77 $c{m}^2$

Area of $△$ACB
=$\frac{1}{2}$$\times$AC$\times$CB
= $\frac{1}{2}$$\times$8.66$\times$11 = 47.63 cm${}^2$
Area of shaded region = 77-47.63 = 29.37 $c{m}^2$.