# 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?

Feb 10, 2016

According to Heron's formula $\sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$, the answer is $\sqrt{12.5 \left(.5\right) \left(9.5\right) \left(2.5\right)}$ 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 $\frac{a + b + c}{2}$.

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)