Re: This building and its rooms have been designated smoke free areas.
Well, it appears the intention there is to include areas of the building that are not considered rooms, such as the lobby, the stairwell, the roof, the entrance, and so on. In that sense, the phrase 'its rooms' makes sense and the sentence stands grammatical, albeit somewhat redundant. A better wording would have been:
- This building has been designated (as) a smoke free environment.