In surveying, what is the term for the area defined by an arc and its endpoints?

The correct term for the area defined by an arc and its endpoints is "segment." In the context of geometry, a segment refers specifically to the region enclosed by an arc on a circle and the straight line that connects the endpoints of that arc. This area lies below the arc and is relevant in various applications, including surveying, where understanding the areas formed by curves is essential for accurate land assessments and calculations.

A sector, on the other hand, is the area enclosed by two radii connecting to an arc, which is distinct from a segment because a sector includes the entire area originating from the center of the circle to the endpoints of the arc, rather than just the area below the arc itself. Fillet is a term used to describe a rounding of a corner or edge, typically in the context of design or construction rather than areas formed by arcs. Tangent refers to a line that touches a curve at exactly one point and does not describe an area or region formed by an arc. Thus, the term segment precisely identifies the specific area bounded by the arc and its endpoints.