# Four hundred meter of fencing are required to enclose a square field .what area can be enclosed by the same length of fencing if the enclosure is circular?

May 1, 2018

$= \frac{40000}{\pi} {m}^{2}$
$\approx 12732.395 {m}^{2}$

#### Explanation:

The length of the fencing is $400 m$. So we must find the area of a circle with circumference$\approx 400 m$. Note that due to the transcendental nature of $\pi$, the exact value cannot be calculated.
$2 \pi r = 400$
$\implies r = \frac{200}{\pi}$

Area of a circle equals $\pi {r}^{2}$
$= \pi {\left(\frac{200}{\pi}\right)}^{2}$
$= \pi \frac{40000}{\pi} ^ 2$
$= \frac{40000}{\pi} {m}^{2}$
$\approx 12732.395 {m}^{2}$