area vs extent

area and extent both are nouns.

Word	Noun	Adjective	Verb	Adverb
area	Yes	No	No	No
extent	Yes	No	No	No

As nouns, extent is a hypernym of area; that is, extent is a word with a broader meaning than area:

area (noun)	extent (noun)
a part of a structure having some specific characteristic or function	the distance or area or volume over which something extends
the extent of a 2-dimensional surface enclosed within a boundary	the point or degree to which something extends
a part of an animal that has a special function or is supplied by a given artery or nerve
a subject of study
a particular geographical region of indefinite boundary (usually serving some special purpose or distinguished by its people or culture or geography)
a particular environment or walk of life