# How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 8, and 22 units in length?

Jan 9, 2016

Heron's formula:
$\textcolor{w h i t e}{\text{XXX}} A r e {a}_{\triangle} = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

#### Explanation:

$s$ is semi-perimeter $= \frac{a + b + c}{2}$ for a triangle with sides $a , b , c$

For the given triangle with $a = 25 , b = 8 , \mathmr{and} c = 22$
$\textcolor{w h i t e}{\text{XXX}} s = 27.5$
and
$\textcolor{w h i t e}{\text{XXX}} A r e {a}_{\triangle} = \sqrt{27.5 \left(2.5\right) \left(19.5\right) \left(5.5\right)}$

$\textcolor{w h i t e}{\text{XXXXXXX}} = 85.87$ (approximately, using a calculator)