GRE Permutation and geometry question?

Question

Are there are formula showing relation between diagonal and no of sides of a polygon?

Answer 1

The formula isYes n(n-3)/2

Answer 2

The number of diagonals in a polygon = n(n-3)/2, where n is the number of polygon sides. For a convex n-sided polygon, there are n vertices, and from each vertex you can draw n-3 diagonals, so the total number of diagonals that can be drawn is n(n-3).