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I would probably do the following:

  1. Run the Lines to polygons tool:

     Vector > Geometry Tools > Lines to polygons
    

Or the Polygonize tool (as suggested by @GaborFarkas@GaborFarkas):

    Processing Toolbox > QGIS Geoalgorithms > Vector geometry tools > Polygonize

  1. Run the Clip tool using the output from Step 1 as the Input layer and your polygon layer as the Clip layer:

     Vector > Geoprocessing Tools > Clip
    

I would probably do the following:

  1. Run the Lines to polygons tool:

     Vector > Geometry Tools > Lines to polygons
    

Or the Polygonize tool (as suggested by @GaborFarkas):

    Processing Toolbox > QGIS Geoalgorithms > Vector geometry tools > Polygonize

  1. Run the Clip tool using the output from Step 1 as the Input layer and your polygon layer as the Clip layer:

     Vector > Geoprocessing Tools > Clip
    

I would probably do the following:

  1. Run the Lines to polygons tool:

     Vector > Geometry Tools > Lines to polygons
    

Or the Polygonize tool (as suggested by @GaborFarkas):

    Processing Toolbox > QGIS Geoalgorithms > Vector geometry tools > Polygonize

  1. Run the Clip tool using the output from Step 1 as the Input layer and your polygon layer as the Clip layer:

     Vector > Geoprocessing Tools > Clip
    
Edited post thanks to @GaborFarkas.
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Joseph
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I would probably do the following:

  1. Run the Lines to polygons tool:

     Vector > Geometry Tools > Lines to polygons
    
  2. Run the Clip tool using the output from Step 1 as the Input layer and your polygon layer as the Clip layer:

     Vector > Geoprocessing Tools > Clip
    

Or the Polygonize tool (as suggested by @GaborFarkas):

    Processing Toolbox > QGIS Geoalgorithms > Vector geometry tools > Polygonize

  1. Run the Clip tool using the output from Step 1 as the Input layer and your polygon layer as the Clip layer:

     Vector > Geoprocessing Tools > Clip
    

I would probably do the following:

  1. Run the Lines to polygons tool:

     Vector > Geometry Tools > Lines to polygons
    
  2. Run the Clip tool using the output from Step 1 as the Input layer and your polygon layer as the Clip layer:

     Vector > Geoprocessing Tools > Clip
    

I would probably do the following:

  1. Run the Lines to polygons tool:

     Vector > Geometry Tools > Lines to polygons
    

Or the Polygonize tool (as suggested by @GaborFarkas):

    Processing Toolbox > QGIS Geoalgorithms > Vector geometry tools > Polygonize

  1. Run the Clip tool using the output from Step 1 as the Input layer and your polygon layer as the Clip layer:

     Vector > Geoprocessing Tools > Clip
    
Source Link
Joseph
  • 76.3k
  • 7
  • 172
  • 286

I would probably do the following:

  1. Run the Lines to polygons tool:

     Vector > Geometry Tools > Lines to polygons
    
  2. Run the Clip tool using the output from Step 1 as the Input layer and your polygon layer as the Clip layer:

     Vector > Geoprocessing Tools > Clip