# How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 29, and 31 units in length?

Feb 25, 2016

$\frac{15 \sqrt{8211}}{4}$

#### Explanation:

The semi-perimeter, $s$, is given by

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

$= \frac{25 + 29 + 31}{2}$

$= \frac{85}{2}$

Now Heron's formula states that the area of the triangle is

$A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

$= \sqrt{\frac{85}{2} \left(\frac{85}{2} - 25\right) \left(\frac{85}{2} - 29\right) \left(\frac{85}{2} - 31\right)}$

$= \frac{15 \sqrt{8211}}{4}$