Trigonometry/Heron's Formula
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Heron's formula states that the area A of a triangle whose sides have lengths a, b, and c is
where is the semiperimeter of the triangle:
There is a proof here.
Exercise
Let's see if Heron's formula works too. And using Heron's formula: It worked. 
The formula is believed to be due to Hero (or Heron) of Alexandria (10 – 70 AD), a Greek mathematician.
Worked Example
so the area of our equilateral triangle is .
And using Heron's formula:
