Area of a triangle

There are several formulas for the area of a triangle. Each depends on what we know about the triangle. For example, the first formula we learn is 1/2 × base × height. That is, if we know the lengths the base (b) and the height (h), we can use the formula

A = ½ bh

to find the area of the triangle.

If we know the lengths of two sides of a triangle and the measure of the included angle, we can use this formula:

A = ½ ab sin q

Last but not least, if we know the lengths of all three sides, we can use what is called the Heron’s Formula: