I am modelling a house in Blender and want to inset the windows. To do that, I thought I would cut out a quadratic hole from the middle of the plane, then extrude the new vertices and create a face from the extruded vertices. I have tried several methods to cut out that hole - using the Knife tool, using a Boolean modifier on the House with a Cube as target, etc. - but all either did nothing, or created two edges between some vertices of the hole and some vertices of the face, like this:
I want to get the above, but without the edges and vertices surrounded in red - I waant to keep only the four vertices (and connecting edges) circled in white. Can this be done ? Please help quickly.