How many ways can we find the area of a triangle?
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Problems in varying levels of mathematics require that the area of a triangle be known, or found.  We  know that there are two formulae for determining the area of a triangle, based upon information that is either given or can be easily determined:
 
The basic formula:

Given:  base and altitude to that base
The trigonometry based formula: 
Given:  two sides and the included angle
 

There is an additional formula, called Heron's formula, that will let you determine the area of a triangle given the lengths of the three sides.  (This formula is often called "Hero's Formula".)

Heron's formula:

where

Given:  the three sides
(s is called the semiperimeter,
or half the triangle's perimeter)

There is also another trigonometric formula.  If two angles and a side are known, the area can be found by using the formula stated below.  The third missing angle is calculated before the formula is used.


Given:  two angles and a side