Hi Knut:
Gryification and Surface Area are two completely different things. Surface Area, as measured by FreeSurfer, gives you the area of the surface (roughly length x breadth) of a given region of interest: e.g., Pars triangularis. It is measured in millimeter squared.
Gyrfication index, by contrast, measures the depth of the each gyri and is done after you have completed the FreeSurfer Recons. You can find more details on gyrification at the following website:
https://surfer.nmr.mgh.harvard.edu/fswiki/LGIThis explains the whole concept of gyrification.