You could try the following
1. Evaluate the surface area with the hole
2. Right click on the hole edge and select delete and the option to Delete holes
3. Evaluate the surface area that has been patched.
4. Subtract the first result from the second for the area of the hole.
5. You can then undo or not save the part to have the original available.
Thanks Ron, not sure if that is faster or not but yes it would work!