Question
In the following 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

We have a square $ABCD$.

We have,
$AB = 22\ cm$
We have to find the perimeter of the triangle. We have a relation as,
Area of circular region $=\frac{1}{5}$ $($Area of $ABCD)$
So,
$\pi\text{r}^2=\frac{1}{2}(22)^2$
$\text{r}=\frac{22}{\sqrt{5\pi}}$
$=5.56$
So perimeter of the circular region,
$=2\pi\text{r}$
$=(2)\frac{22}{7}\Big(\frac{22}{\sqrt{5\pi}}\Big)$
$=34.88\text{cm}$

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