metropolitan area vs principal city

metropolitan area

noun
  • An area of population usually with a central or core city and surrounding towns or suburbs. 

principal city

noun
  • Synonym of central city (“the main city of a metropolitan area; particularly one containing multiple cities”). 

  • Used other than figuratively or idiomatically: see principal, city. 

How often have the words metropolitan area and principal city occurred in a corpus of books? (source: Google Ngram Viewer )