# How do you use Heron's formula to determine the area of a triangle with sides of that are 6, 5, and 8 units in length?

Apr 18, 2016

≈ 14.98 square units

#### Explanation:

This is a 2 step process.

Step 1
Calculate half the perimeter (s) of the triangle.

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

let a = 6 , b = 5 and c = 8

$\Rightarrow s = \frac{6 + 5 + 8}{2} = \frac{19}{2} = 9.5$

Step 2

Calculate the area (A) using

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

$\Rightarrow A = \sqrt{9.5 \left(9.5 - 6\right) \left(9.5 - 5\right) \left(9.5 - 8\right)}$

 = sqrt(9.5xx3.5xx4.5xx1.5) ≈ 14.98" square units "