Key:way area
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The key way_area is a synthetic key created by osm2pgsql during import for Mapnik. It is calculated by the get_area function.
The unit of the area depends on how the data was imported, if it was with osm2pgsql -l (latlon), it will be square degrees, otherwise square meters.
Note of warning: the square meters are projected square meters. With the default Spherical Mercator projection, this means that same sized areas appear larger in the way_area column the further from the equator they are.