Filtering features using geometric attributes of polygons in ArcGIS Desktop?

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Given a polygon featureclass containing many polygons of different sizes and shapes, which geometric attributes (area, perimeter, etc) could be used to filter the polygons? It's probably best to ask this in two parts:

1. Which geometric attributes do polygons possess?
2. How would you calculate these attributes? Geoprocessing tools/ArcObjects preferred, but I would be satisfied with conceptual calculations which could then be coded.

As an example, I am considering calculating the maximum length of a polygon by breaking the edge of the polygon into points at a small interval and then calculating the distance between all points - the longest distance would be the maximum length of that polygon.

I'm hoping to use these attributes to allow interactive user control of polygon filtering.



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