# A triangle has sides with lengths: 6, 11, and 9. How do you find the area of the triangle using Heron's formula?

##### 1 Answer

Jan 5, 2016

#### Explanation:

First, find the triangle's semiperimeter. The semiperimeter is one half the perimeter of the triangle, which can be represented for a triangle with sides

#s=(a+b+c)/2#

Thus,

#s=(6+11+9)/2=13#

Now, use Heron's formula to determine the area of the triangle. Heron's formula uses only the side lengths of the triangle to find the triangle's area:

#A=sqrt(s(s-a)(s-b)(s-c))#

#A=sqrt(13(13-6)(13-11)(13-9))#

#A=sqrt(13xx7xx2xx4)#

#A=2sqrt182#