Question

a farmer has 100m of fencing and he needs to make the biggest plot of land with no gaps what is the biggest plot of land the farmer can make?
please show working out

Answer 1

Circles occupy the maximum area for a given perimeter. This can be showed by looking at the change in enclosed area for regular n sided figure with a given perimeter. It appears that as n increases, the enclosed area increases. The extreme of this is that n becomes infinite and the figure becomes a circle.
Now,
\[P = 2 \pi r \Rightarrow r = \frac{P}{2 \pi} \Rightarrow A = \pi r^2 = \frac{P^2}{4 \pi}\]
\[ Area enclosed = \frac{10000}{4 * 3.14} = 796.18 m^2 \]

Answer 2

thanks that helps :)