How do you find the minimum,average, and maximum width of a polygon?

Question

Given a list of vertices

Answer 1

Under what conditions?

Knowing the perimeter?

Knowing the area?

Or do you mean just for a given polygon?

If so, what kinds of polygon?

Answer 2

♠ find a circle of max radius that fits in your polygon - the diameter being the minimal width;
♣ find area A of your polygon, admit A being the area of a circle A=pi*D^2/4, hence diameter D=4A/pi is average width;
♦ find a circle of min radius into which your polygon fits - the diameter being the maximal width;