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,
[tex]\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[/tex]
