How many diagonals in a 2-dimensional equilateral figure?

Answer 1

The number of diagonals in an equilateral figure can be calculated from the number of sides.

If the number of sides is "S", then the number of diagonals would be S(S-3)/2

This becomes clear if you consider that there will be the same number of vertices as there are sides. From each vertex you can draw a diagonal to all vertices except the one you started from and the two adjacent ones (lines between the adjacent vertices and the starting point are sides of the figure, not diagonals). This gives you S·(S-3) but that would double count the diagonals since each diagonal can start at either vertex.