Heron's Formula

If the base and corresponding altitude of a triangle are known, you can find the area of a triangle. However, sometimes you are not given the altitude (height) corresponding to the given base of a triangle. Instead, you are given the three sides of the triangle.

In this case also, you can find the height (or altitude) corresponding to a side and calculate its area. However, the process involved in the solution is lengthy. To help us in this matter, a formula for finding the area of a triangle with three given sides was provided by a Greek mathematician Heron (75 B.C. to 10 B.C.).

$$ \text{Area of a triangle} = \sqrt{s(s - a)(s - b)(s - c)} $$

where, a, b and c are the three sides of the triangle and 

$$ s = \frac{a + b + c}{2} $$