How do you calculate the area of a triangle? Chances are, you'll answer, "One-half times the base times the height." True that...but this is only one formula for the area of a triangle. Did you know that there are many others? Sometimes, you don't know the base length and the height of the triangle. Then you'll have to use a different method. Heron's Formula is one such method.
Use Heron's Formula when you know the lengths of all three sides of the triangle. The formula states that the area, A, of a triangle with side lengths a, b, and c is
where s is the semiperimeter (half the perimeter) of the triangle:
To use Heron's Formula, first use the second equation to find s. Then use that value of s (along with a, b, and c) to calculate A.
What is the area of a right triangle with side lengths 3, 4, and 5? Try calculating this both using the A=(1/2)(base)(height) formula and by using Heron's Formula. Hopefully, you will obtain the same answer both times!
Honestly, from my experience, Heron's Formula is rarely used in Mathcounts competitions. There is usually an easier way to calculate the area of a given triangle. I can virtually guarantee that you won't need Heron's Formula at the School or Chapter levels; I've seen it in one problem at the State level; possibly, it's used more at the National level.
But it never hurts to learn something new!