If it's simple length x width just create a parameter and export to custom iproperty.
You may possibly be able to extract the sheet metal area.
But I'm not sure about the total surface area directly.
This may be possible through ilogic or vba.
Try the following: (In this case, the data displayed in the parts list is m²; playing around with the units will allow you to get the unit of measurement you want.)
Create a new user parameter called "Area", set units to m.
Create an iLogic rule, copy and paste the following:
In Document Settings, set linear dim precision to 2.12 (Units tab), then set the base qty to Area (BOM tab).
The unit of measurement displayed in the parts list will be m (as opposed to m²), however the value will give you the area in m².
Hope this helps!