# How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 16, and 12 units in length?

Apr 11, 2016

Area of triangle is $107.32$ units.

#### Explanation:

If three sides of a triangle are $a$, $b$ and $c$, according to Heron's formula its area is given by

$\sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$, where $s = \frac{1}{2} \left(a + b + c\right)$ is semi perimeer of the triangle.

In the given triangle the three sides are $15$, $16$ and $12$ and semi perimeter is $\frac{1}{2} \times \left(15 + 16 + 12\right) = \frac{1}{2} \times 43 = 21.5$.

Hence area is given by

$\sqrt{22.5 \left(22.5 - 15\right) \left(22.5 - 16\right) \left(22.5 - 12\right)}$

or $\sqrt{22.5 \times 7.5 \times 6.5 \times 10.5} = \sqrt{11517.1875} = 107.32$