Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 12, 3, and 10 units in length?

Answer 1

According to Heron's formula `sqrt(s(s-a)(s-b)(s-c))`, the answer is `sqrt(12.5(.5)(9.5)(2.5))` which roughly equals 12.18.

Explanation:

To find the area of a triangle using Heron's formula, you must first find the semi-perimeter or s in the equation.

Here `s` is equal to the sum of all three sides of the triangle all divided by `2`, or `(a + b + c)/2`.

You then plug it into `s` in the formula and then find the differences between the three sides and the semi-perimeter. Multiply the differences with the semi-perimeter and square root the result to find the area of the triangle. (Wikipedia)