3'x5' and 2'x3' oriental rugs can often be found for a song. Use a few of them to cover the floors of halls, entryways, and other connecting spaces that have a more irregular layout.
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Consider what opportunities lie inside of your corners. Is it possible you could carve out a niche like in this example? You could turn it into a home office, a bar or simply a space to corral toys. If such a renovation is within your budget, it could prove to be a lifesaver.
the closed area over the desk. Maybe with some piano hinges so they can be open sometimes. But in general I think that I want everything closed so it looks neat and tidy.