1. The altitude of a triangle
In the case of a triangle, a common way to calculate its area is 'half base times height' where the 'height' is the
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 at right angles to it.
For more on this see
2. An altitude of a triangle
An altitude is also a line which passes through a vertex of a triangle, and is at right angles to the opposite side.
A triangle has three altitudes.
An interesting fact is that the three altitudes always pass through a common point called the orthocenter of the triangle.
Orthocenter of a triangle
3. 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.
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
Definiton and properties of a trapezoid (coordinate geometry) including altitude and median
Definition and properties of triangles
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