# How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 6, and 13 units in length?

Jan 23, 2016

$A r e a = 38.678$ square units

#### Explanation:

Heron's formula for finding area of the triangle is given by
$A r e a = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

Where $s$ is the semi perimeter and is defined as
$s = \frac{a + b + c}{2}$

and $a , b , c$ are the lengths of the three sides of the triangle.

Here let $a = 15 , b = 6$ and $c = 13$

$\implies s = \frac{15 + 6 + 13}{2} = \frac{34}{2} = 17$

$\implies s = 17$

$\implies s - a = 17 - 15 = 2 , s - b = 17 - 6 = 11 \mathmr{and} s - c = 17 - 13 = 4$
$\implies s - a = 2 , s - b = 11 \mathmr{and} s - c = 4$

$\implies A r e a = \sqrt{17 \cdot 2 \cdot 11 \cdot 4} = \sqrt{1496} = 38.678$ square units

$\implies A r e a = 38.678$ square units