This is the 10144th most frequent Polish word.
bogatej
The Polish word "bogatej" means "rich" or "wealthy" (feminine, singular, genitive/dative/locative case).
'Bogatej' is used here as an adjective in dative case modifying the feminine noun 'rodzinie'.
Bogatej rodzinie zawsze łatwiej jest podróżować.
A wealthy family always finds it easier to travel.
'Bogatej' is used as an adjective in genitive case modifying the feminine noun 'historii'.
To jest opowieść o bogatej historii tego miasta.
This is a story about the rich history of this city.
'Bogatej' is an adjective in genitive case modifying the feminine noun 'rezydencji'.