Question

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

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

Answer 1

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

$Areaofsquare=a^2=2^2=4c{m}^2$

$Radiusofsemicircle=\left(2/2\right)=1cm$

$Areaoftwosemicircles=Areaofonecircle=\pi \times \left(1\right)\left(1\right)=\pi c{m}^2$

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