basearea

Basearea is a term used in geometry to denote the area of the base face of a three-dimensional object. The base is the designated face that serves as a reference for measuring the object's height, and the base area is the two-dimensional measure of that face. The concept is especially important for solids described by a base and an extruded or extended height, such as prisms and pyramids.

In prisms, the volume is the product of the base area and the height (the perpendicular distance between the bases). In pyramids, cones, and other solids formed by tapering from the base to an apex, the volume is one third of the base area times the height.

To compute a base area, use formulas appropriate to the base shape. For a polygon, straightforward methods include triangulation or the shoelace formula. For a circular base with radius r, the base area is πr^2. For a regular polygon with n sides and side length s, the area is (n s^2) / (4 tan(π/n)).

In more general contexts, base area refers specifically to the area of the planar region lying in the base plane of the solid; changes in the side surfaces do not affect the base area itself.