# How do you use Heron's formula to find the area of a triangle with sides of lengths 9 , 5 , and 8 ?

Feb 2, 2016

$A = 19.9$ rounded to one decimal place

#### Explanation:

Heron's formula is $A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$, where $s$ is the semiperimeter of the triangle, which is half of its perimeter.

Let $a = 9$, $b = 5$, and $c = 8$.

$s = \frac{9 + 5 + 8}{2}$

$s = \frac{22}{2}$

$s = 11$

Substitute the known values into Heron's formula.

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

$A = \sqrt{11 \left(11 - 9\right) \left(11 - 5\right) \left(11 - 8\right)}$

Simplify.

$A = \sqrt{11 \left(2\right) \left(6\right) \left(3\right)}$

Simplify.

$A = \sqrt{396}$

$A = 19.9$ rounded to one decimal place