How do you find the area of a triangle? The formula is ½ base times height. Sounds easy enough, but what do you do if you the height is unknown? Here is where Heron’s formula saves the day. Heron’s formula has been around forever and it helps you find the height of a triangle if you know the length of all three sides. Here is the formula and then we will look at an example.
The first step in using Heron’s formula is finding S. In order to find S you add the lengths of the three sides and divide this number by two. Notice, it is not an average of the numbers.
Step1 Assign values to the sides of the triangle 6=a 8=b 12 =c
Step 2 Take the square root of 13( 13-6)(13-8)(13-12) = 13(7)(5)(1)
Step 3 Which equal’s the square root of 455 = 21.33 units squared
Therefore,the area of the triangle equals 21.33 units squared
For additional information see Heron's Formula