arena vs theater

arena

noun
  • The building housing such an area; specifically, a very large, often round building, often topped with a dome, designated for indoor sporting or other major events, such as concerts. 

  • The sand-covered centre of an amphitheatre where contests were held in Ancient Rome. 

  • An enclosed area, often outdoor, for the presentation of sporting events (sports arena) or other spectacular events; earthen area, often oval, specifically for rodeos (North America) or circular area for bullfights (especially Hispanic America). 

  • A realm in which events take place; an area of interest, study, behaviour, etc. 

theater

noun
  • A place or building, consisting of a stage and seating, in which an audience gathers to watch plays, musical performances, public ceremonies, and so on. 

  • A conspicuous but unproductive display of action. 

  • Any place rising by steps like the seats of a theater. 

  • An operating theatre or locale for human experimentation. 

  • A cinema. 

  • Drama or performance as a profession or art form. 

  • A region where a particular action takes place; a specific field of action, usually with reference to war. 

  • A lecture theatre. 

How often have the words arena and theater occurred in a corpus of books? (source: Google Ngram Viewer )