It is strange that, since the beginning of SketchUp, this hasn’t been picked up by the developers, maybe because there were area-extensions since version 4.
Anyway, an Area-attribute in Generate Report would be on my wish list (like Quantities), as well as a distinction between different units in the entity info (mm for length, m2 for area, HL for volume)
And since the icon is a bucket, why not have an extra attribute, l/m2, set how many liters you have, and see when the bucket is empty while painting!
(Or is this covered with an extension, as welll)