Probably considerably less than that once you account for all the costs associated with awarding contracts. Including "bidding" and multi layer sub contracting. Even if the whole thing is free from any kind of bribary.
I just upgraded my office (12 Ubiquiti access points, covering 45,000 square feet - probably about the average size of a school campus)
Area is rather less meaningful than number/density of clients. Also schools typically have what is effectivly a whole site shift change every hour or so. Schools tend to "punch above their weight" in comparison to businesses when it comes to things like network bandwidth requirements.
Even though Unify is cost effective both in terms of the prices of access points and not requiring a separate management system if it's not on some "approved list" a school may not be able to buy it with this money anyway. Also in a school environment you'd most likely be looking at at least one access point per room for decent coverage.