Question

The side of a square is 2 cm and semicircles are constructed on each side of square then the area of the whole figure is

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

Given the side of square is 2 cm

Then the area of square =$2\times 2=4$

And Semi circle are constructed on each side

Then four sides of square constructed four semi circles of radius half of side of square=1 cm

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

So area of four semicircle=$4\times \frac{\pi }{2}=2\pi$sqcm

So total area of figure =$4+2\pi$ sq cm