How can I calculate geometrical features of polygon (perimeter and area) per zone (similar to zonal stats for rasters)? I have a square fishnet (approx 20x35, 1 square kilometer each) and I need to calculate forest area and boundary length per each zone.
Assuming that your fishnet has a field whereby you are able to distinguish between individual gridsquares(i.e. a unique ID field or name), use union (Analysis Tools > Overlay > Union) to overlay both datasets. Once complete, update your area field (right-click, Calculate Geometry). Then use Dissolve (Data Management Tools > Generalisation > Dissolve) using two fields (i.e. your grid ID and land cover of your choosing), this will simplify your attribute table by sequentially listing the gridsquare number and all features of forest.
Calculating perimeter lengths within gridsquares is then simply a Calculate Geometry operation in the attribute table but using the Perimeter property in the Calculate Geometry window.