A supplement to Ian's answer: Here is the largest-area sofa known,
due to Gerver:
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![GerverSofa][1]
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> Gerver, Joseph L. (1992). "On Moving a Sofa Around a Corner". *Geometriae Dedicata* 42 (3): 267–283. ([Springer link](http://link.springer.com/article/10.1007/BF02414066).)


  [1]: https://i.sstatic.net/FBlms.png