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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.

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Are you aware of zonal geometry? –  whuber May 25 '12 at 15:27
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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.

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Thank you. Here is another way to calculate perimeter (after conversion polygon->line): link –  0x29a May 26 '12 at 9:53
    
Unfortunately it says that only registered users can access your link. Are you able to summarise? –  veedub May 28 '12 at 9:13
    
Sorry for delay. Here is Google Cache copy for posterity: goo.gl/mrCiS –  0x29a Dec 23 '12 at 0:22
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You may use Tabulate Area tool in Zonal Statistics aswell. I find it quite useful to calculate histograms for a specific zone.

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