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( (180)/(n) \right)\quad \begin{cases} n=\textit{number of sides}\\ s=\textit{length of a side}\\ (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( (180)/(100) \right)\implies A=25cot\left((9)/(5)^o \right) \\\\\\ A\approx 795.51289884`