proof of heronze formula
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Algebraic Proof of Heron's formula which is also called as hero's formula is given above:
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The demonstration and proof of Heron's formula can be done from elementary consideration of geometry and algebra. I will assume the Pythagorean theorem and the area formula for a triangle

where b is the length of a base and h is the height to that base.

We have

so, for future reference,
2s = a + b + c
2(s - a) = - a + b + c
2(s - b) = a - b + c
2(s - c) = a + b - c