# How do you use Heron's formula to find the area of a triangle with sides of lengths 9 , 5 , and 12 ?

Jan 21, 2016

Use Heron's formula to find area $A = 4 \sqrt{26} \approx 20.396$

#### Explanation:

Heron's formula gives the area $A$ of the triangle in terms of its sides $a$, $b$, $c$ and semi-perimeter $s = \frac{a + b + c}{2}$ as:

$A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

In our example, $a = 9$, $b = 5$, $c = 12$, $s = \frac{a + b + c}{2} = 13$ and:

$A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

$= \sqrt{13 \cdot 4 \cdot 8 \cdot 1} = \sqrt{416} = 4 \sqrt{26} \approx 20.396$