In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, a base is a
side of a
polygon or a
face of a
polyhedron, particularly one oriented
perpendicular
In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can ...
to the direction in which
height
Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is).
For example, "The height of that building is 50 m" or "The height of an airplane in-flight is ab ...
is measured, or on what is considered to be the "bottom" of the figure. This term is commonly applied to
triangle
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, any three points, when non- colli ...
s,
parallelograms,
trapezoids,
cylinders
A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.
A cylinder may also be defined as an infini ...
,
cones,
pyramids,
parallelepipeds and
frustums.
Role in area and volume calculation
Bases are commonly used (together with heights) to calculate the
area
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while ''surface area'' refers to the area of an open su ...
s and
volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). Th ...
s 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.
Extended bases in trigonometry
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
perpendicular
In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can ...
ly
intersect
Intersection or intersect may refer to:
* Intersection in mathematics, including:
** Intersection (set theory), the set of elements common to some collection of sets
** Intersection (geometry)
** Intersection theory
* Intersection (road), a pl ...
the extended opposite base (but not the base proper).
See also
*
Apex (geometry)
In geometry, an apex (plural apices) is the vertex which is in some sense the "highest" of the figure to which it belongs. The term is typically used to refer to the vertex opposite from some " base". The word is derived from the Latin
Lati ...
References
{{reflist
Parts of a triangle
Area
Volume