# How do you use Heron's formula to determine the area of a triangle with sides of that are 7, 4, and 9 units in length?

Jan 19, 2016

$A = 4 \sqrt{15}$

#### Explanation:

Heron's formula states the the area of a traiangle $A$ can be calculated as
$A = \sqrt{p \left(p - a\right) \left(p - b\right) \left(p - c\right)}$ where $p = \frac{a + b + c}{2}$ and $a$, $b$ and $c$ are the three sides of the triangle.

So for this example
$p = \frac{7 + 4 + 9}{2} = 10$

$A = \sqrt{10 \left(10 - 7\right) \left(10 - 4\right) \left(10 - 9\right)} = \sqrt{10 \cdot 4 \cdot 6 \cdot 1} = \sqrt{240}$

$A = \sqrt{16 \cdot 15} = 4 \sqrt{15}$