"The pencil and the sharpener are in the pencil case."
Translation:Creionul și ascuțitoarea sunt în penar.
In general, the definite article isn't used when you are using a preposition. So, while in English we would say that "The cat is on the table", in Romanian we would say "Pisica este pe masă." (The cat is on table.) As for why it's like that, that's just how it is in Romanian. That's what makes it fun. :)
I can't speak for "în penarul rosu"--I'm not sure what makes that definite, but "în nordul orasului" nord is definite because that's the genative case, and you can't have something indefinite "owned" by something else in genative. ("the north of the city")
(Well, you can, but you have to use helper words to make it happen. "A cat of the man" would be "O pisică a omului". The "a" after pisică is a definite article all by itself that makes it okay grammatically." I was taught it as the "ale mamei tale" rule, where "some cats of your mom's" would be "niște pisici ale mamei tale".)