I have been checking Gamow's question and noticed something! If we draw all diagonals there is a little polygon in the middle of the original polygon if it is odd-gon (odd-gon is defined as the number of vertices is an odd number.). For example;
So if you draw a regular pentagon on a piece of paper and draw all diagonals, there is a new pentagon in the middle of our original pentagon (shown as darker).
The area-ratio between the small and original pentagon is 6.854.
Question 1: What is the area-ratio between the small and original 99-gons of 99-gon where 99 is number of vertices of the polygon?
Question 2: Is there any formula that you can derive for the area-ratio between the small and original x-gons of x-gon where x is number of vertices of the polygon?