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I am looking for a tool in ArcGIS 10.1 QGIS or R that allows me to count the number of polygons that are inside specific areas (defined also as polygons).

My data consists of: one shapefile with multiple polygons with different shapes and sizes, and one shapefile with the zone/areas

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    Do you mean you want to count any part of any polygons that intersect with the polygon that defines the specific area? Or must they be fully inside the specific area polygon i.e. "whole" polygons? – SlowLearner Aug 21 '13 at 19:37
  • Take a look at the rgeos R package. There are numerous topology overlay functions that would address variations of this question. – Jeffrey Evans Dec 31 '17 at 18:49
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In ArcGIS: Execute these steps, only using your polygon feature class instead of the point feature class mentioned in the link.

Note that this will only work properly if your "outer" polygons do not overlap. Since you are talking about zoning areas, they should not overlap.

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