# How do you use Heron's formula to determine the area of a triangle with sides of that are 8, 7, and 10 units in length?

Jul 26, 2016

$\text{Area"_triangle ~~27.81" sq. units}$

#### Explanation:

According to Heron's formula, for a triangle with sides of lengths $a , b ,$ and $c$
the area of the triangle is
color(white)("XXX")"Area"_triangle =sqrt(s * (s-a) * (s-b) * (s-c))

where $s$ is the semi-perimeter; that is $s = \frac{a + b + c}{2}$

For a triangle with the given lengths $7 , 8 ,$ and $10$
$\textcolor{w h i t e}{\text{XXX}} s = 12.5$
and
color(white)("XXX")"Area"_triangle = sqrt(12.5 * 5.5 * 4.5 * 2.5)

$\textcolor{w h i t e}{\text{XXXXXXX}} = \sqrt{773.4375}$

$\textcolor{w h i t e}{\text{XXXXXXX}} \approx 27.81$