In geometry, a base is a side of a polygon or face of a polyhedron, particularly one perpendicular to the direction height is measured or on what is considered to the bottom of the object. This usage can be applied to a triangle, parallelogram, trapezoid, cylinder, cone, pyramid, parallelepiped or frustum. By extension, the length or area of a figure's base is also called its base. As such, bases are commonly used in formulas for area and volume. For example, a formula for the area of a triangle is (1/2) × base × height. Another example is an octagonal prism; its base is an octagon, and its volume is the area of the base times the height.
The extended base of a triangle (a particular case of an extended side) is the line that contains the base. The extended base is relevant in the context of an obtuse triangle: the altitudes from the acute angled vertices are exterior to the triangle and perpendicularly intersect the opposite base but not the base itself, and one of those altitudes can be treated as the height of the triangle in the above formula for its area.
- Palmer, C.I.; Taylor, D.P. (1918). Plane Geometry. Scott, Foresman & Co. pp. 38, 315, 353.
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