While there is no simple formula to determine area for most quadrilaterals, and most polygons for that matter, we saw last section that for the special quadrilaterals parallelograms and trapezoids there are specific formulas for determining area. The area of a triangle, however, does. This is why it is so important that any polygon can be divided into a number of triangles. The area of a polygon is equal to the sum of the areas of all of the triangles within it.

The area of a triangle can be calculated in three ways. The most common expression for the area of a triangle is one-half the product of the base and the height (1/2AH). The height is formally called the altitude, and is equal to the length of the line segment with one endpoint at a vertex and the other endpoint on the line that contains the side opposite the vertex. Like all altitudes, this segment must be perpendicular to the line containing the side. The side opposite a given vertex is called the base of a triangle. Here are some triangles pictured with their altitudes.