baseheight

Baseheight is a term used to describe the height of a geometric figure measured perpendicular to a chosen base. The concept is not intrinsic to a figure by itself; the base must be specified, and changing the base can change the corresponding height.

In two dimensions, baseheight is most familiar in triangles. The area of a triangle is one half the product of a chosen base and the corresponding height, where the base is any side and the height is the perpendicular distance from the opposite vertex to that base. For polygons, height can be defined with respect to different bases when using decomposition into triangles or when applying base-height formulas to special shapes.

In three dimensions, baseheight often refers to the distance between two parallel base faces of a prism or the perpendicular distance from a plane to a point. For a prism, the height is the perpendicular distance between its base faces. In other solids, one may define the height relative to a selected base plane, which is useful for calculating volumes, projections, or cross-sections.

Calculation and interpretation rely on coordinate or geometric definitions of distance. In coordinate form, the height is the length of the perpendicular segment from a point to a line (2D) or from a point to a plane (3D). Understanding baseheight emphasizes that height depends on the chosen base, and different bases yield different heights for the same figure.

See also: altitude, perpendicular distance, base (geometry), area, volume.