Base (geometry)

In geometry, a base is a side of a polygon or a face of a polyhedron, particularly one oriented perpendicular to the direction in which height is measured, or on what is considered to be the "bottom" of the figure.

[1] This term is commonly applied in plane geometry to triangles, parallelograms, trapezoids, and in solid geometry to cylinders, cones, pyramids, parallelepipeds, prisms, and frustums.

The side or point opposite the base is often called the apex or summit of the shape.

The area of a triangle is its half of the product of the base times the height (length of the altitude).

the area is: Given a fixed base side and a fixed area for a triangle, the locus of apex points is a straight line parallel to the base.

Bases are commonly used (together with heights) to calculate the areas and volumes of figures.

By this usage, the area of a parallelogram or the volume of a prism or cylinder can be calculated by multiplying its "base" by its height; likewise, the areas of triangles and the volumes of cones and pyramids are fractions of the products of their bases and heights.