"The district is in the zone."
Translation:Η περιφέρεια είναι μέσα στην ζώνη.
Sometimes, "...μέσα στον/στη(ν)/στο..."="...στον/στην/στο...".
The students are in the classroom=Οι μαθητές είναι (μέσα) στην τάξη.
Unless stated otherwise, finding students inside a classroom is the norm, so "μέσα" can be omitted. Same goes for "...(πάνω) στον/στη(ν)/στο...".
Ι'm really sorry to be so bolshy, but this means practically nothing in British English - I think it might to the Americans out there. We don't have districts in zones. In fact, we don't talk much about zones at all. I write English language learning materials and we are not allowed to use examples which are not usable, however much it suits the exercise grammatically or any other way.
I suppose the probability of encountering this sentence would be rather low in Greek, but this sentence makes me think of different ticket zones with different prices for the "red", "blue", "green" one etc. Something like "The neighborhood we want to go to is in that zone, so we'll have to pay that much to get there".