One genreally accepted way of measuring irregular polygons is to get the extream length, and then find the perpendicular width half way between the ends. That is how I approached the problem for a system I built a couple years ago.
I took the polygon, and generated a near table for points created from all the verticies. I then found the maximum length, and the pair of points to which that length referred.
I genereated a line between these points (the length of the polygon), then rotated the line 90° and clipped it with the polygon. The length of that clipped line is the width.
With this method, the length is exact, and is the greatest overall length. The width is a conventional width. It worked for me because I was most concerned with the extream length and was content to approximate the width.
You could use the length line (before rotation) to perform another near distance calculation to find the polygon vertex points furthest from that line in either direction. Adding the two distances (furthest distance to the left and furthest to the right) gives the overall width of the polygon, square to the longest dimension line.