Originally Posted by
Prove It First of all, it would help if you wrote the length of each side as a fraction, as they are exact.
$\displaystyle \displaystyle \begin{align*} x &= 0.363636\dots \\ 100x &= 36.363636\dots \\ 100x - x &= 36.363636\dots - 0.363636\dots \\ 99x &= 36 \\ x &= \frac{36}{99} \\ x &= \frac{4}{11} \end{align*}$
So that means each side is $\displaystyle \displaystyle \begin{align*} \frac{4}{11} \end{align*}$ of a unit in length, and since there are 11 sides, the perimeter is $\displaystyle \displaystyle \begin{align*} 11 \times \frac{4}{11} = 4 \end{align*}$ units.