Question

proof herons formula​

Answer 1

Answer:

Heron's Formula -- An algebraic proof

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

There is at least one side of our triangle for which the altitude lies "inside" the triangle. For convenience make that the side of length c. It will not make any difference, just simpler.



Let p + q = c as indicated. Then 









Step-by-step explanation:

I hope it will help you a lot

Answer 2

Step-by-step explanation:

For any triangle, the only way heron's formula = (S^2 sqrt(3)) / 4 is for the trivial case where S = 0. So no, it cannot simplify in general the way you propose. If indeed the triangle is equilateral, then a=b=c and then Heron's simplifies to: A = sqrt[S(S-a)^3] assuming all sides are a.

Hope it's help uh ❤️