I have several worn areas of high traffic ( 3 areas appx. 10sq. ft. each) on the kitchen with red oak floor. The floor is about 7 years old.
Question: Can I have just these areas refinished or do I have to refinish the entire kitchen and adjacent areas (800 sq. ft)?

You will need to do the entire space. It is possbile to cut off certain rooms if the flooring is running the right way.

Thank you RhodesHardwood. I suspected that that, but hoped to find a less expensive solution. What should I expect to pay for 750 sq. ft.?

My pricing starts at $1.70 per square foot and can go up from there depending on degree of difficulty as well as the type of finish that is speced out for the job. A typical range for sanding and finishing with three coats of oil urethane should be between $1.50 to $2.50 pre square foot. It's possible to find much higher prices as well.