# How do you use Heron's formula to find the area of a triangle with sides of lengths 6 , 4 , and 8 ?

Feb 15, 2016

Heron's formula uses the lengths of the sides and the semiperimeter to find the area of a triangle

The formula is given as $\sqrt{\left(s\right) \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

Where $s = \frac{a + b + c}{2}$

With this information, it should be easy to plug in the numbers to find the area

First, find s

$\frac{6 + 4 + 8}{2}$ =====> $s = 9$

Now plug this into Heron's formula

$\sqrt{\left(9\right) \left(9 - 6\right) \left(9 - 4\right) \left(9 - 8\right)}$

$\sqrt{\left(9\right) \left(3\right) \left(5\right) \left(1\right)}$

$\sqrt{135}$

This cannot be simplified any furthur. So we are done.