I have a L shaped house and want to put an addition that make the house a square.

Does the foundation have to square or can it be just along the outside.

Footers Just along the outside new perimeters are fine unless there is a load bearing wall of the new addition against the actual house for some reason. That can be eliminated to if a beam carried that load to the adjacent walls with footers Other wise a 3 sided footer is fine to make the square

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Changing an L shaped house to a square will be difficult from the roofing point of view unless you have a flat roof. The other issue is that the former outside walls of the L will be load bearing when you add the extra square room to fill the 'L' in - meaning that it may be difficult to come up with a room plan that you like. These are just things to consider before you get to far along with your plans.

A much easier expansion route may be to extend either end of the L.