# A triangle has sides with lengths: 16, 11, and 19. How do you find the area of the triangle using Heron's formula?

Jun 21, 2016

≈ 87.91 square units

#### Explanation:

This is a 2 step process.

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

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{s = \frac{a + b + c}{2}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where a , b and c are the 3 sides of the triangle.

here let a = 16 , b = 11 and c = 19

$\Rightarrow s = \frac{16 + 11 + 19}{2} = \frac{46}{2} = 23$

Step 2: Calculate area (A ) using the following

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

$A = \sqrt{23 \left(23 - 16\right) \left(23 - 11\right) \left(23 - 19\right)}$

=sqrt(23xx7xx12xx4)≈87.91" square units"