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

Jan 5, 2016

$A = 2 \sqrt{182}$

#### 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 $a , b ,$ and $c$ as

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

Thus,

$s = \frac{6 + 11 + 9}{2} = 13$

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:

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

$A = \sqrt{13 \left(13 - 6\right) \left(13 - 11\right) \left(13 - 9\right)}$

$A = \sqrt{13 \times 7 \times 2 \times 4}$

$A = 2 \sqrt{182}$