Living rooms are flexible depending on how you intend to lay the rug but there are two common positions which lend themselves well to comfortable arrangements.
The first would be to use a rug that would run the length of the couch such as a 5’ x 6’, 5’ x 7’ or a 6’ x 9’. With a relatively smaller rug, you can brighten up a conversation area without paying for space that would otherwise be covered by furniture.
Another common arrangement would be to use a large room sized rug such as an 8’ x 10’ or 9’ x 12’ and having some furniture hang off the sides of it. While a larger rug may be covered partially by furniture you remain open to many design possibilities that may not be possible with a smaller rug.