What is the number of sides of a regular polygon for which the number of diagonals is or ?
Source: NCTM Mathematics Teacher 2006
The number of diagonals of a convex polygon of vertices (or sides) is given by . Please refer to post titled “Convex Polygon” posted on 6/18/2011 for details.
Case 1: diagonals
Let’s try a few numbers
The polygon has sides.
Case 2: diagonals
Continuing where we left off above we get
Clearly, there is no polygon that has diagonals.