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Base
One side of a polygon, usually used as a reference side for other measurements.
Most often used with triangles.
Triangles
In the case of a triangle, a common way to calculate its area is 'half of base times height' where the 'height' is the altitude, or the perpendicular distance from the base to the opposite vertex.
Triangle showing its base and altitude
The base can be any side, not just the one drawn at the bottom. To calculate the area you must use the altitude that is at right angles to the chosen base. Choose any convenient side to be the base. In an isosceles triangle, the base is usually taken to be the unequal side.
For more on this see Triangle definition, and Area of a triangle
Quadrilaterals with a pair of parallel sides
If a quadrilateral has a pair of parallel sides, both of them are called a base. And just like triangles, the altitude of such a figure is the perpendicular distance from a base to the opposite side. You can pick either base as your starting point.
Parallelogram showing bases
For more on this see
(C) 2007 Copyright John Page