How can I determine if a certain polygon falls within another separate polygon using QGIS?

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Another option is to use the Spatial Query tool from the Vector menu.

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Enter your source layer & reference/ intersect layer, and specify "within" as the criterion. If you want to only run the query using selected features of either layer, select these before running the query.

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If you wish, you can then use the button shown below to create a new layer from the resulting selection.

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The new layer is then added to the table of contents window. You can then right click on the layer name and "save as" if desired.

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Add your polygon layers and then go to Vector>Research Tools>Select By Location. Set your parameters accordingly and make sure to check the 'Within' box for the Geometric predicate, and run it.

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