Question: how many triangles can be formed by joining the vertices of a regular polygon with 20 sides?
Answer: There are 20c3= 1140 ways to choose three vertices that form a triangle. Of these, there are 20 triangles with two side lengths on the perimeter of the regular polygon. Also, for each side, there are 16 points that can make a triangle with exactly one side length on the 20-gon.