whilst i don't understand "area density" ...
one way (very olde school) would be to apply a body force (say 1g down) and the reaction would equal the weight;
another (an artfull combination of new and old) would be to 3D print your part, immerse it in water, to determine it's volumne ...;
another would be to ask the cad program that created the part "what's the volume?" and take it from there.
another day in paradise, or is paradise one day closer ?