Question:
A circular field has a perimeter of 650 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.
Solution:
We have a circular field in which a square field is marked.
Let the radius of the circle be r. We have,
Perimeter $=650$
$r=\frac{325}{\pi}$
Use Pythagoras theorem to find the side of square as,
$\mathrm{AB}=\sqrt{r^{2}+r^{2}}$
$=\frac{325}{\pi} \sqrt{2}$
So area of the square plot,
$=(\mathrm{AB})^{2}$
$=\left(\frac{325}{\pi} \sqrt{2}\right)^{2} \mathrm{~m}^{2}$
$=\left(\frac{325(7)}{22} \sqrt{2}\right)^{2} \mathrm{~m}^{2}$
$=21387 \mathrm{~m}^{2}$