In geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, a base is a side of a plane figure or face of solid, particularly one perpendicular to the direction height

Height

Height is the measurement of vertical distance, but has two meanings in common use. It can either indicate how "tall" something is, or how "high up" it is. For example "The height of the building is 50 m" or "The height of the airplane is 10,000 m"...

 is measured or on what is considered to the bottom. This usage can be applied to a triangle

Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....

, parallelogram

Parallelogram

In Euclidean geometry, a parallelogram is a convex quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure...

, trapezoids, cylinder

Cylinder (geometry)

A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder...

, pyramid

Pyramid

A pyramid is a structure whose outer surfaces are triangular and converge at a single point. The base of a pyramid can be trilateral, quadrilateral, or any polygon shape, meaning that a pyramid has at least three triangular surfaces...

, parallelopiped or frustum

Frustum

In geometry, a frustum is the portion of a solid that lies between two parallel planes cutting it....

. By extension, the length or area of a base is also called a base. As such, bases are commonly used in formulas for area

Area

Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

 and volume

Volume

Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

.

Of the three sides of an isosceles triangle, the one which is not one of the two equal sides is called the base.