# How do you use Heron's formula to find the area of a triangle with sides of lengths 8 , 3 , and 9 ?

Feb 4, 2016

A~~11.8" square units rounded to one decimal place.

#### Explanation:

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

$s = \frac{a + b + c}{2}$, where $a = 8 , b = 3 , \mathmr{and} c = 9$.

$s = \frac{8 + 3 + 9}{2}$

Simplify.

$s = \frac{20}{2}$

$s = 10$

Heron's Formula

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

Substitute the known values into the equation and solve.

A=sqrt(10(10-8)(10-3)(10-9)

Simplify.

$A = \sqrt{\left(10\right) \left(2\right) \left(7\right) \left(1\right)}$

$A = \sqrt{140}$

A~~11.8" square units rounded to one decimal place.