Final answer:
The property system described, entailing individual ownership combined with shared community space, is characteristic of a planned community or homeowners' association (HOA).
Step-by-step explanation:
The student asks about a property system where the owner has rights to their individual house and land, as well as common interests in communal areas like recreation areas, trails, and a clubhouse. This most likely describes ownership in a planned community or homeowners' association (HOA).
In these arrangements, individuals own their private property but also share rights and responsibilities concerning common property, which are often governed by the association's rules and regulations. Easements may provide rights to use the property, and zoning regulations could influence how land is used and developed within the community.