# How do you use Heron's formula to determine the area of a triangle with sides of that are 12, 7, and 10 units in length?

Feb 7, 2016

$A = \frac{\sqrt{210}}{2} s q . c m$

#### Explanation:

Heron's formula

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

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

$s = \frac{12 + 7 + 10}{2}$
$s = \frac{19}{2}$
$A = \sqrt{\frac{19}{2} \left(\frac{19}{2} - 7\right) \left(\frac{19}{2} - 12\right) \left(\frac{19}{2} - 10\right)}$
$A = \sqrt{\frac{12}{2} \left(\frac{14}{2}\right) \left(- \frac{5}{2}\right) \left(- \frac{1}{2}\right)}$
$A = \sqrt{\frac{840}{16}}$
$A = \frac{2 \sqrt{210}}{4}$
$A = \frac{\sqrt{210}}{2} s q . c m$