If the space is a 10x10 square as you suggest, I would use a round or square rug, or even an octagonal one might work, with approximately an 8 foot width/diameter.

I vote for a round rug -- as large as possible -- maybe one of the 9ft. ones?

Thanks for the advice!

try_hard
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I vote for a square rug.

I'm assuming your table has no extension leaves but if it does then I'd go for an 8 x 10 rug ( in reality they're usually 7'6" x 9'6")

I would make a square rug out of Flor tiles -- you can make it exactly the size you need, and if food gets it on it, you can take a tile out to wash or, if necessary, replace.

Here is a link that might be useful: Flor carpet tile

I vote for a round one. Everything in our homes is so angular, our rooms need curves to soften them.

big and round here too.

Here's a picture of my nook with it's still-undecorated walls.

I like the square rug because it defines the space where 2 more walls would be. Extending that logic, perhaps a square rug would make your space feel too closed-in, especially if the doorway is narrow. In that case I would say go round or octagonal.

The table is 48" in diameter, the chairs are smaller than today's chairs and the walls are 7 and 7.5 feet. Hope this helps.