Why not try a circular rug right under a square table.
Round table on square rug.
Visually a round rug works better in a square space than a rectangular space and you might like to create two separate areas within a large living room.
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Round table round rug.
Round rug is ideal for a square table like that minimizes corners but leaves room for chairs to push out.
A rug should visually relate to whatever sits on over or near it.
Square table square rug i have no idea if that is an official rule or not as i am not school trained in design.
As long as the rug is big enough.
For example a round dining table and a round rug below speak the same design lingo while a square rug and bold boxy light.
Setting off a round table with a square rug gives the room some geometric variety and grounds the table in the room.