# How do you use Heron's formula to find the area of a triangle with sides of lengths 4 , 8 , and 5 ?

Feb 12, 2016

$A = 8.1815$

#### Explanation:

Heron's formula is A=sqrt(s(s-a)(s-b)(s-c), where $A$ is area, $a , b , \mathmr{and} c$ are the sides, and $s$ is the semiperimeter, which is the perimeter divided by $2$. Side $a = 4$, side $b = 8$, and side $c = 5$.

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

$s = \frac{4 + 8 + 5}{2}$

$s = \frac{17}{2}$

$s = 8.5$

Use Heron's formula to find the area of the triangle.

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

Substitute the known values into the equation.

A=sqrt((8.5)(8.5-4)(8.5-8)(8.5-5)

Simplify.

A=sqrt((8.5)(4.5)(0.5)(3.5)

Simplify.

$A = \sqrt{66.9375}$

Take the square root.

$A = 8.1815$ square units to four decimal places.