Outdoor Amphitheater

We are working on a project with 4000 seat outdoor, but covered, amphitheater with a 20,000 s.f. back of house/administrative building. We are probably going to completely rebuild the building component, but will keep a modified seating and roof above the amphitheater in place. The site is about twice as large as the footprint of the building and amphitheater. Can you advise whether it would make more sense to include the entire site in the site boundary for this project or just the building itself? We are struggling with defining exactly what the outdoor covered amphitheater is in terms of LEED language. Any advice would be appreciated.