An n-sided polygon has n sides and n vertices.
Every diagonal and every side of the polygon is the line segment
connecting a combination of two vertices.
Every combination of 2 vertices uniquely represents either a side
or a diagonal.
Derivation of the formula:
1. First we get the number of sides and diagonals by getting the
number of combinations of n vertices taken 2 at a time:
C(n,2) =
2. To get the number of diagonals only, we must subtract the number
of sides, which is n.
- n
3. We get an LCD of 2 and simplify:
- =
So if d represents the number of diagonals of
an n-sided polygon, then the formula is
d =
Edwin