# How do you use Heron's formula to find the area of a triangle with sides of lengths 12 , 5 , and 8 ?

Jan 24, 2016

$A r e a = 14.52369$ 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 $a = 12 , b = 5$ and $c = 8$

$\implies s = \frac{12 + 5 + 8}{2} = \frac{25}{2} = 12.5$

$\implies s = 12.5$

$\implies s - a = 12.5 - 12 = 0.5 , s - b = 12.5 - 5 = 7.5 \mathmr{and} s - c = 12.5 - 8 = 4.5$
$\implies s - a = 0.5 , s - b = 7.5 \mathmr{and} s - c = 4.5$

$\implies A r e a = \sqrt{12.5 \cdot 0.5 \cdot 7.5 \cdot 4.5} = \sqrt{210.9375} = 14.52369$ square units

$\implies A r e a = 14.52369$ square units