hero's formula?

Question

how do you derive the hero's formula that is used to find the area of a triangle of given sides

Answer 1

There are two formulas that can be used to get the area of a triangle. One is:
(Base*Height)/2
However, the height cannot always be detected. There is a formula called hero's formula which helps us find the area with just the sides of a triangle. Here is the derivation:
Let a,b and c be the sides of a triangle. Let s be the semiperimeter of the triangle.
s = (a+b+c)/2
Area of the triangle = [(s)(s-a)(s-b)(s-c)]^(1/2)
(or)
= Square root of [(s)(s-a)(s-b)(s-c)]

Answer 2

http://en.wikipedia.org/wiki/Heron%27s_formula#Proof


Doug

Answer 3

Go here: http://www.karlscalculus.org/hero.html