Question

What is the area of a regular polygon with 100 sides and a perimeter of 100 units?

Answer 1

Now, if the regular polygon has 100 sides, and the perimeter is 100 units, that simply means that each side is 1 unit, foot, meter, else.

so, we know each side is 1 unit long, and we know there are 100 sides,

$\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2cot\left( \frac{180}{n} \right)\quad \begin{cases} n=\textit{number of sides}\\ s=\textit{length of a side}\\ \frac{180}{n}=central~angle\\ \qquad~~ in~degrees\\ ----------\\ n=100\\ s=1 \end{cases} \\\\\\ A=\cfrac{1}{4}\cdot 100\cdot 1^2\cdot cot\left( \frac{180}{100} \right)\implies A=25cot\left(\frac{9}{5}^o \right) \\\\\\ A\approx 795.51289884$