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

Area of the square $=a^2=4c{m}^2$
Radius of the semi-circle formed $=$ 1 cm
Area of the 2 semi-circles $=2\left(\frac{\pi }{2}{r}^2\right)=2\left(\frac{\pi }{2}\right)=\pi c{m}^2$
Total Area$=4+\pi c{m}^2$