# How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 18, and 12 units in length?

$16 {S}^{2} = \left(a + b + c\right) \left(- a + b + c\right) \left(a - b + c\right) \left(a + b - c\right) = \left(15 + 18 + 12\right) \left(- 15 + 18 + 12\right) \left(15 - 18 + 12\right) \left(15 + 18 - 12\right) = \left(45\right) \left(15\right) \left(9\right) \left(21\right) = 3 \left(15\right) \left(15\right) \left(9\right) \left(3\right) \left(7\right)$ or
$S = \frac{9 \left(15\right)}{4} \sqrt{7} = \frac{135 \sqrt{7}}{4}$