Question

If in the rectangle ABCD, AB is a diameter of semicircle and BC is its radius equal to 7 cm. Find the area of shaded region.

• A. 11 cm
• B. 14 cm
• C. 21 cm
• D. 22 cm

Answer 1

The correct option is C 21 cm

Given :
Consider the rectangle ABCD
AB = Diameter = Length
BC = Radius = Breadth

We know diameter = 2$\times$radius
diameter = 2$\times$7 = 14 = AB = CD

Area of rectangle ABCD
= length$\times$breadth
= diameter$\times$radius
= 14$\times$7 = 98 $c{m}^2$

Area of semicircle = $\frac{1}{2}$$\times$$\pi$$r^2$
= $\frac{1}{2}$$\times$$\frac{22}{7}$$\times$$7^2$
= $\frac{1}{2}$$\times$$\frac{22}{7}$$\times$$7^2$ = 77 $c{m}^2$

Area of shaded region
= Area of rectangle ABCD - Area of semicircle
Area of shaded region= 98-77 = 21 $c{m}^2$