proof of 'heron's formula' using trigonometry

In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle when the length of all three sides are known. Unlike other triangle area formulae, there is no need to calculate angles or other distances in the triangle first.

1) find area of equilateral triangle inscribed in square

2) proof of baudhayana proof/Pythagoras proof

3). proof of distance formula

4) Garfield proof of Pythagoras

5) find area of triangle inscribed in semicircle

6) find length

[mikeoxmaul]

2:48 when you carried the bc under the root. Where did the negative bc squared come from?

Edit: I'm trying to use your method to prove heron's formula for my project. Please help.