Science Buddies: "Ask an Expert"

Is there any point in analyzing Heron's Formula to get useful results? If not, could you please suggest other formulas, postulates, or theorems that would work? Thanks.

Hi gogopoco,,

That's an interesting formula you bring up, one that I hadn't heard of despite majoring in mathematics many eons ago.

Heron's formula has a practical use: one can compute the area of a triangle while measuring only the lengths of the three sides. The wikipedia entry for Heron's formula:

http://en.wikipedia.org/wiki/Heron's_formula

has the formula and two proofs.

Two other sources of information are at:

http://mathworld.wolfram.com/HeronsFormula.html
http://www.mathopenref.com/heronsformula.html

The second reference above has an interactive Heron's formula calculator.

Thanks for the help. but I don't know if it's useful to anaylze different ways of proving Heron's Formula. Could you please help me?

Hi gogopoco,

I agree, the proof of Heron's formula is not of practical value. What is of practical value is the formula itself. It's good to know that there is a proof of the formula (and the proof has stood the test of time). The proof allows you to apply the formula to calculate area with a certainty that the returned area value is correct.

It's not necessary to understand the proof or be able to reproduce it in a test. (And the proof is not at a grade 6-8 level.) Note: in the discussion above, "proof" refers to "proofs" (since there are two).

Hi Gogopoco! Are you looking at Heron's formula for a science fair project, or for a class assignment, or for a test in school? Let us know what has been asked of you, and we will better be able to answer your question.

laura

It's for a science fair project.
One last question: If Heron's Formula is not practical to analyze, do you know any other formulas that would produce useful results through an analysis of them?

Hi gogopoco,

Some websites with formulas are:

http://www.ma.utexas.edu/users/kawasaki ... form1.html
http://engr.astate.edu/jdg/Circuits/Lab ... mulas.html (for Electric Circuits)

Do these help?

Hi gogopoco,

Heron's Formula is useful, it can be used to calculate a triangle's area knowing only the lengths of the sides.
For example, in the classic right triangle with sides of lengths:
3, 4, 5

Heron's formula says the area of the triangle (here sides a, b, c) is:

SQRT(s*(s-a)*(s-b)*(s-c)), where SQRT is the square root and
s is the semiperimeter of the triangle: (a+b+c)/2
In the 3,4,5 triangle, s = (3+4+5)/2 = 6

According to Heron's formula the area of the triangle is:
SQRT(6*(6-3)*(6-4)*(6-5))=SQRT(6*3*2*1)=SQRT(36)=6

The other way of computing the area is:
since the triangle has sides 3, 4, 5, it is half of a rectangle with sides 3 and 4. The area of the rectangle is 12 (3*4). The area of the triangle is 6.

So both ways of computing the area match!