Base (geometry)

The base of any geometric figure is (for polygons) any side that you wish to measure from or, (for polyhedra), any face that you wish to measure from. Bases are most commonly used in geometric formulas for area and volume. It is most commonly represented by the variable $b$. To distinguish side lengths from areas of bases in three-dimensional figures, the capital letter "B" often replaces "b" in signifying the area of a base.

Examples

The formula for the area of a triangle:

$A=frac\{1\}\{2\}bh,$

where $b$ is the length of the side from which you measure your perpendicular height ($h$).

The formula for the volume of a cone:

$V=frac\{1\}\{3\}Bh,$

The volume of the cone is the area of the base multiplied by one-third the height of the cone, where $B$ is the area of the circular face of the cone.

For many three-dimensional figures, including cylinders, prisms, and polyhedra, the volume is simply the area of the base multiplied by the figure's height:

V=Bh

It is important to note that a geometrical base is perspective-dependent. For example, there is no single base on a scalene triangle. The formula for the area will stay consistent, however, because the height of the triangle is also variable depending on which side of the triangle is chosen as the base. For equilateral triangles, each side is equal; it therefore does not matter from which side a height is measured.

For some three-dimensional figures there is only one base, e.g. a cone, or it does not matter which base is chosen, e.g. a right circular cylinder.

The base in geometry is essential to determining the volume of certain polyhedra. A highly irregular, concave polygon may be the base of a prism; if the area of that base is known, the volume of the prism is also known.

ee also

*Area
*Volume