# How do you use Heron's formula to find the area of a triangle with sides of lengths 8 , 4 , and 9 ?

May 23, 2018

See below

#### Explanation:

Heron formula is $S = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$ where

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

In our case $s = \frac{8 + 4 + 9}{2} = \frac{21}{2}$

Now $S = \sqrt{\frac{21}{2} \left(\frac{21}{2} - 8\right) \left(\frac{21}{2} - 4\right) \left(\frac{21}{2} - 9\right)} =$

=sqrt(21/2·5/2·13/2·3/2)=sqrt(4095/16)=(3sqrt455)/4 square units