How do you use Heron's formula to determine the area of a triangle with sides of that are 12, 18, and 19 units in length?

Jun 15, 2016

≈104.635 square units

Explanation:

This is a 2 step process.

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

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{s = \frac{a + b + c}{2}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where a , b and c are the sides of the triangle

let a = 12 , b = 18 and c = 19

$\Rightarrow s = \frac{12 + 18 + 19}{2} = \frac{49}{2} = 24.5$

Step 2: Calculate the area (A ) using

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

$= \sqrt{24.5 \left(24.5 - 12\right) \left(24.5 - 18\right) \left(24.5 - 19\right)}$

=sqrt(24.5xx12.5xx6.5xx5.5)≈104.635" square units"