I think an 8 x 10 would look much better there.

Why do you need a rug right there? A floating rug is not going to look right.

8x10' minimum

Are there rugs in the dining room and living room?

Can you post other angles, and how it relates to the neighboring rooms? From this photo, it reminds me more of a pass-through or walkway than an actual seating area. If that’s the case, I’d do a runner ... as if it was an entry or hallway. But without seeing more, it’s hard to say.

ETA: OTOH, I have seen many homes with large open/connecting rooms with big rugs. So it’s really personal preference and decor style.