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I have some irregularly shaped polygons existing within an Esri geodatabase. What does the 'shape_length' field represent geometrically? i.e. Does it represent the furthest distance between two points?

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It represents the total length of the polygon's perimeter, in the units used by the feature class' coordinate system. So if your feature class is in UTM meters, the length will be in meters (if the coordsys is geographic, the units will be in Cartesian degrees, i.e., useless).

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