qgis - Convert a line to polygon

I have a shapefile with city areas but unfortunately the shapefile only contains single lines. The shapefile looks like this:

I want to convert those lines to an area-polygon shapefile in QGIS. I tried it with the "Lines to polygons" tool (Vector > Geometry Tools > Lines to polygons), but it didn't work correctly. After using this tool the shapefile looks like this:

Is there any other way to convert the line shapefile to an area polygon shapefile in QGIS?

By the way, I am using QGIS 2.14.3 Essen.