Base
A base is one side of a polygon, usually used as a reference side for other measurements.
Most often used with triangles.
1. In 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.
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
2. 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. For example, in a parallelogram:
For more on this see
3. Faces of a solid
One or two
faces
of a solid are sometimes called a base. For example a
pyramid
has one base, and a
cylinder
has two parallel bases:
The altitude of a triangle is the perpendicular from a vertex to the opposite side.
The conventional method of calculating the area of a triangle (half base times altitude) with pointers to other methods and special formula for equilateral triangles
Definition and properties of triangles
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