I would put a rug with the seating area of with the sectional. I you have more then one sitting area you could do another to define the area.

Yes, you would want to do two rugs. They will define each space and allow you to keep the traffic areas open. I would start with a rug under the sectional, it will warm up that space and will give it a more complete look. Then you can take your time and find a second coordinating one under the dining table. But definitely two, not one, the room is just too large for one. Good, luck, your room looks really cool:)