# How do you use Heron's formula to find the area of a triangle with sides of lengths 19 , 14 , and 13 ?

Feb 4, 2016

The area of the triangle would be $55.3 u n i t {s}^{2}$

#### Explanation:

First we would find S which is the sum of the 3 sides divided by 2.

$S = \frac{19 + 14 + 13}{2}$ = $\frac{46}{2}$ = $23$

Then use Heron's Equation to calculate the area.

$A r e a = \sqrt{S \left(S - A\right) \left(S - B\right) \left(S - C\right)}$

$A r e a = \sqrt{23 \left(23 - 19\right) \left(23 - 14\right) \left(23 - 13\right)}$

$A r e a = \sqrt{8.5 \left(4\right) \left(9\right) \left(10\right)}$

$A r e a = \sqrt{3060}$

$A r e a = 55.3 u n i t {s}^{2}$