rural area vs geographical area

rural area and geographical area both are nouns.

Word	Noun	Adjective	Verb	Adverb
rural area	Yes	No	No	No
geographical area	Yes	No	No	No

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

Other hypernyms of rural area include geographic area, geographic region, geographical region.

rural area (noun)	geographical area (noun)
an area outside of cities and towns	a demarcated area of the Earth