# How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 16, and 13 units in length?

May 2, 2018

$\text{area "~~91.192" to 3 dec. places}$

#### Explanation:

$\text{the area (A) of a triangle using "color(blue)"Heron's formula}$ is.

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

$\text{where s is the semi-perimeter and a, b, c the sides of }$
$\text{the triangle}$

$\text{let "a=15,b=16" and } c = 13$

$\Rightarrow s = \frac{15 + 16 + 13}{2} = \frac{44}{2} = 22$

$\Rightarrow A = \sqrt{22 \left(22 - 15\right) \left(22 - 16\right) \left(22 - 13\right)}$

$\textcolor{w h i t e}{\Rightarrow A} = \sqrt{22 \times 7 \times 6 \times 9}$

$\textcolor{w h i t e}{\Rightarrow A} = \sqrt{8316} \approx 91.192$