Question

What is Heron's formula?

Answer 1

Heron's formula allows you to evaluate the area of a triangle knowing the length of its three sides.
The area `A` of a triangle with sides of lengths `a, b` and `c` is given by:

`A=sqrt(sp×(sp-a)×(sp-b)×(sp-c))`

Where `sp` is the semiperimeter:

`sp=(a+b+c)/2`

For example; consider the triangle:

The area of this triangle is `A=(base×height)/2`
So: `A=(4×3)/2=6`
Using Heron's formula:
`sp=(3+4+5)/2=6`
And:
`A=sqrt(6×(6-5)×(6-4)×(6-3))=6`

The demonstration of Heron's formula can be found in textbooks of geometry or maths or in many websites. If you need it have a look at:
http://en.m.wikipedia.org/wiki/Heron%27s_formula

Answer 2

Heron's Formula is usually the worst choice for finding the area of a triangle.

Explanation:

Alternatives:

Area `S` of a triangle with sides `a,b,c`

`16S^2=(a+b+c)(-a+b+c)(a-b+c)(a+b-c)`

Area `S` of a triangle with squared sides `A,B,C`

`16S^2 = 4AB-(C-A-B)^2=(A+B+C)^2-2(A^2+B^2+C^2)`

Area of a triangle with vertices `(x_1, y_1), (x_2, y_2), (x_3, y_3)`

`S = 1/2 | (x_1- x_3)(y_2 - y_3) - (x_2 - x_3)(y_1 - y_3)| = 1/2 | x_1 y_2 - x_2 y_1 + x_2 y_3 - x_3 y_2 + x_3 y_1 - x_1 y_3 |`

Oh yeah, Heron's Formula is

`S = sqrt{s(s-a)(s-b)(s-c)}` where `s=1/2(a+b+c)`