Are sad at heart in one part of the country (4)

I believe the answer is:
area
'country' is the definition.
(thesaurus)
'are sad at heart in one part' is the wordplay.
I cannot quite understand how this works, but
an anagram of 'are' is 'rea' which is present in the answer.
'one' could be 'a' (a thing is one thing) and 'a' is located in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
'of the' is the link.
Can you help me to learn more?
(Other definitions for area that I've seen before include "District; locale" , "Region, space" , "Succession, order" , "Speaking formally to (someone)" , "Space for a specific purpose, say picnic" .)