You could create a quilt of the outside surfaces and measure the area of the quilt. To create a quilt you can select one of the surfaces on the outside of the model,hold your shift key down and select other "bounding surfaces". This will collect all surfaces starting at the first surface selection ("the seed") and stop at any bounding surfaces. If you want all outside surfaces and there are no holes in the part, you could select the same surface as the seed and the boundary. Once you have all the surfaces selected, simply select, copy, and paste. A "Copy" feature should be created in your model tree that is a "Quilt" containg all the surfaces selected. Then select, analysis, measure, area and select the quilt.
