2020-sided Polygon

Since there are so many sides, we can assume that the regular polygon is a circle. Then the perimeter is the circumference or

$2\pi r = 2 \pi \cdot \sqrt{\frac {365}\pi} = 2 \cdot \sqrt{365\pi} \approx 67.725$

The same answer up to three decimal places. So need no formula when the sides are many .

I don't know if what I did was right, but I assumed a $2020-$ gon as a circle!

$\pi r^2 =365 \implies r \approx 10.778$ $\implies 2\pi r \approx \boxed{67.72}$

The formula to get the area of a regular polygon is:

$\large A = \frac{1}{4}ns^{2} \cot\left(\frac{π}{n}\right)$ $\small \begin{array}{lcl} n & = & \text{the number of sides of the polygon.} \\ s & = & \text{side length of the polygon.} \end{array}$

$\small \begin{array}{cccl} & 365 & = & \dfrac{1}{4}(2020)(s^{2}) \cot\left(\dfrac{π}{2020}\right) \\[1em] \implies & s & = & \dfrac{2 \sqrt{365} \sqrt{\tan \left( \dfrac{π}{2020} \right) }}{ \sqrt{2020}} \\[1em] & s & \approx & 0.033527 \end{array}$

Multiplying the side length by $2020$ , we get the perimeter $\boxed{\approx 67.725}$ .