# How do you use Heron's formula to find the area of a triangle with sides of lengths 18 , 9 , and 13 ?

Feb 22, 2016

Heron's formula relates the area of a triangle to the side of the triangle

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

Where s is the sum of the side lengths divided by 2.

So, first we find s, the semiperimeter

$18 + 9 + \frac{13}{2} = 20$

So $s = 20$

Now we simply plug in the values into Heron's formula

$A = \sqrt{\left(20\right) \left(20 - 18\right) \left(20 - 9\right) \left(20 - 13\right)}$

$A = \sqrt{\left(20\right) \left(2\right) \left(11\right) \left(7\right)}$

$A = \sqrt{3080}$

$A = 2 \sqrt{770}$

which is approximately 55.5