A circular field has a perimeter of $ 650 \mathrm{~m} $. A square plot having its vertices on the circumference of the field is marked in the field. Calculate the area of the square plot.

Given:

A circular field has a perimeter of \( 650 \mathrm{~m} \). A square plot having its vertices on the circumference of the field is marked in the field. 

To do: 

We have to calculate the area of the square plot.

Solution:

Perimeter of the circular field $= 650\ m$

This implies,

Radius of the field $(r)=\frac{\text { Circumference }}{2 \pi}$

$=\frac{650 \times 7}{2 \times 22}$

$=\frac{2275}{22} \mathrm{~m}$

Therefore,

Diagonal of the inscribed square $=$ Diameter of the circle

$=2r$

$=2 \times \frac{2275}{22}$

$=\frac{2275}{11} \mathrm{~m}$

Side of the square $=\frac{\text { Diagonal }}{\sqrt{2}}$

$=\frac{2275}{\sqrt{2} \times 11}$

Area of the square field $=a^{2}$

$=(\frac{2275}{11 \sqrt{2}})^{2}$

$=\frac{5175625}{121 \times 2}$

$=21386.88$

$\approx 21387$

The area of the square plot is $21387\ m^2$.

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Updated on: 10-Oct-2022

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