Question

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

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

We know that area of semi circle of radius $r$ is $\frac{\pi r^2}{2}$ and area of square od side $a$ is $a^2$

Given that:

Side of square $=2cm$

Total area $=$ Area of square$+4\times$Area of semi circle

Total area $=2^2$$+4\times \frac{\pi \times 2^2}{2}$

$=(4+8\pi )c{m}^2$