English question, please help.?

What do you call the area with some apartment bulidings that is taken care of by the same security guards? (you know what I mean)

For example, I live in an apartment. And I want to say, "we have a lot of trees in our (apartment bulidings area). Or we have a swimming pool in (our apartment buildings district)?

What do you call this, and how do you say it properly in a common way? Thanks. Deeply appreciated.