I have a polygon representing the extent of a study area. This polygon is overlaid to a raster representing the quality of land, which is classified into 5 classes (from bad  to good ). I would like to have arcGIS (10.1, advanced license) calculate how much land within the polygon is bad, how much is mediocre, and so on. How can I accomplish this?
You may use Zonal Histogram. As Input raster of feature zone data, specify your polygon(s). As Input value raster, the land quality raster. The output table will show each land quality class as a row, each polygon class as a column. Thus if you have more than one polygon, you may want to group them into classes beforehand, using a unique value for each class in a special column. This column is specified as the Zone field in the tool. An alternative is to select only the polygon you are interested in and only then run the tool.