Question

The side of a square is 2 cm Semicircles are constructed on two sides of the square then the area of the whole figure is

• A. $(4+\pi )c{m}^2$
• B. $(4+4\pi )c{m}^2$
• C. $4\pi c{m}^2$
• D. $8\pi c{m}^2$

Answer 1

The correct option is A $(4+\pi )c{m}^2$

The side of square is 2 cm

Then area of square =$(2{)}^2=4c{m}^2$

The Semicircle constructed on two side diameter 2 cm then radius =1 cm

Then area of one semicircle =$\frac{\pi r^2}{2}=\frac{\pi (1{)}^2}{2}=\frac{\pi }{2}$

Then area of two semicircle=$2\times \frac{\pi }{2}=\pi$

So total area of whole figure=$(4+\pi )c{m}^2$