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 to triangles,
parallelograms,
trapezoids,
cylinders,
cones,
pyramids,
parallelepipeds and
frustums.

Bases are commonly used (together with heights) to calculate the areas and volumes of figures. In speaking about these processes, the measure (length or area) of a figure's base is often referred to as its "base."

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. Some figures have two parallel bases (such as
trapezoids and frustums), both of which are used to calculate the extent
of the figures.^{2}

The **extended base** of a triangle (a particular case of an extended
side) is the
line that contains the base. The extended
base is important in the context of obtuse
triangles: the
altitudes from the
acute vertices
are external to the triangle and
perpendicularly
intersect the extended opposite base (but not
the base proper).

Original source: base (geometry). Shared with Creative Commons Attribution-ShareAlike 3.0 License

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