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?

1 Answer

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.


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)