that is for rectangles. Take an isoceles triangle, rotate it by 22.5 degrees, assume that the base is 1 unit but the lengths of the sides are unknown. Yes... I can manually do the 'math'. but lets assume you have 1000000 irregular shapes and need to get a measure of the 'length' and 'width' of the shape. There is no such thing for a convex or concave polygon, however one can fit a Minimum Area Bounding Rectangle to the shape, from which you get the characteristic long and short axes. From this you get the area of the rectangle... you can then calculate the actual area and perimeter From there you can calculate all kinds of 'shape' geometric properties... area/area ratios, MABR perimeter/shape perimeter etc etc. So unless you are working with pure geometric properties with only a couple of shapes, then you can either do the 'math' by hand, do all kinds of field calculations or use the results of existing tools.
Also by calculating the enclosing circle, MABR and convex hull, you enter a whole new level of shape descriptors. I haven't even mentioned the Minimum Area Bounding Ellipse that can also be thrown in. The geometric shapes that can be calculated and classed as containers are quite extensive in number and they each have their own purpose. Don't limit yourself to hand calculations or simple geometry when assessing what tools are useful, because you will encounter a situation where you might have gained some useful information by applying existing tools to new problems.
