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Areas Related to Circles — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsAreas Related to Circles2 Marks
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 = 22cm, find:
The circumference of the central part.
✓

Answer

We have a square ABCD.

We have,
AB = 22cm
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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