# A triangle has sides with lengths: 16, 8, and 19. How do you find the area of the triangle using Heron's formula?

Dec 26, 2015

(see below for method)
Approximate area $63.2$

#### Explanation:

Heron's Formula tells us that if we are given a triangle with sides $a , b , c$ and a semi-perimeter $s = \frac{a + b + c}{2}$, the area of the triangle is:
color(white)("XXX")"Area"_triangle = sqrt(s(s-a)(s-b)(s-c))

For the given values $\left(a , b , c\right) = \left(16 , 8 , 19\right)$
$\textcolor{w h i t e}{\text{XXX}} s = \frac{43}{2}$

$\textcolor{w h i t e}{\text{XXX}} \left(s - a\right) = \frac{11}{2}$
$\textcolor{w h i t e}{\text{XXX}} \left(s - b\right) = \frac{27}{2}$
$\textcolor{w h i t e}{\text{XXX}} \left(s - c\right) = \frac{5}{2}$

Applying the formula (and using a calculator)
color(white)("XXX")"Area"_triangle ~~63.2