What is the proper term for a floor that extends beyond the lower portion of the house?

The term that accurately describes a floor that extends beyond the lower portion of the house is "cantilever." A cantilever is a structural element that is anchored at one end and projects horizontally beyond its support, creating an overhanging effect. This design is commonly used in architecture and construction to create balconies, decks, or other protruding features on a building.

Cantilevers are engineered to withstand the forces acting on them, such as gravity and wind load, while maintaining structural integrity. This makes them particularly appealing for modern designs that seek to create open and airy spaces without visible supporting columns underneath.

While other terms may refer to different aspects of building elements—like "overhang" which could describe any projection from the building itself, such as roof eaves, or "balcony," which typically refers to a platform that extends from the facade of a building and is usually surrounded by a railing—"cantilever" specifically applies to the scenario where a structural element is unsupported on one end. Therefore, "cantilever" is the most precise term in the context of a floor extending beyond the house.