# How do you use Heron's formula to find the area of a triangle with sides of lengths #6 #, #4 #, and #9 #?

##### 1 Answer

Mar 10, 2016

#### Explanation:

For a triangle with side

#s = frac{a+b+c}{2}#

Heron's formula states that the area of the triangle is given by

#"Area" = sqrt{s(s-a)(s-b)(s-c)}#

In this question, we have

#a=6# #b=4# #c=9#

The semi-perimeter,

#s = frac{6+4+9}{2} = 19/2#

So, the area of the triangle is

#"Area" = sqrt{19/2(19/2-6)(19/2-4)(19/2-9)}#

#= frac{sqrt{1463}}{4}#

#~~ 9.562#