Question

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

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

Answer 1

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

Area of whole figure $=$ Area of square + 4 $\times$ area of semicircle

$={\left(2\right)}^2+4\times \frac{1}{2}\times \pi \times {\left(\frac{2}{2}\right)}^2$

$=(4+2\pi ){cm}^2$