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Altitude
The vertical distance from one side of a figure (its base) to the opposite side or vertex.
Loosely: the 'height' of the figure.
Triangles
In the case of a triangle, a common way to calculate its area is '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 pick one side to be the base, and then measure the altitude that is at right angles to it.
For more on this see
Quadrilaterals with a pair of parallel sides
If a quadrilateral has a pair of parallel sides, both of them are called a base. In a similar way to triangles, the altitude of such a figure is the perpendicular distance from a base to the opposite side. Since they are parallel, either one will do.
Note: A common mistake is to use the length of the slanted side as the altitude. This is wrong. You must use the vertical distance as shown above.

See these pages for examples of the use of altitudes:
(C) 2007 Copyright John Page