Question

In given figure, the square ABCD is divided into five equal parts, all having same area. The central part is circular and the lines AE, GC, BF and HD lie along the diagonals AC and BD of the square. If AB = 22 cm, find the circumference of the central part.

Answer 1

Given $AB=BC=CD=DA=22cm$

Area of square$=22\times 22=484c{m}^2$

Area of circle$=\frac{1}{5}\times 484=96.8c{m}^2$ (It is given circle is divided into 5 equal parts)

$\Rightarrow \pi r^2=96.8\Rightarrow r^2=\frac{96.8}{3.14}=30.83\Rightarrow r=\sqrt{30.83}=5.55cm$

Circumference$=2\pi r=2\times 3.14\times 5.55=34.854cm$