# How do you use Heron's formula to determine the area of a triangle with sides of that are 6, 4, and 8 units in length?

Jun 12, 2016

≈ 11.62 square units

#### Explanation:

This is a 2 step process.

Step 1: calculate half the sum (s ) of the perimeter

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{s = \frac{a + b + c}{2}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

let a = 6 , b = 4 and c = 8 ( the sides of the triangle)

$\Rightarrow s = \frac{6 + 4 + 8}{2} = \frac{18}{2} = 9$

Step 2: calculate the area (A ) using

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$A = \sqrt{9 \left(9 - 6\right) \left(9 - 4\right) \left(9 - 8\right)}$

=sqrt(9xx3xx5xx1)=sqrt135≈11.62 (2 "decimal places")