# How do you use Heron's formula to find the area of a triangle with sides of lengths 14 , 9 , and 13 ?

May 27, 2018

$\textcolor{b l u e}{\text{Area"=18sqrt(10)" square units}}$

#### Explanation:

Heron's Formula is given as:

"Area=sqrt(s(s-a)(s-b)(s-c))

Where $a , b \mathmr{and} c$ are the lengths of the triangles sides.

$s = \text{semiperimeter} = \frac{a + b + c}{2}$

Let: $a = 14$, $b = 13$. $c = 9$

Then:

$s = \frac{14 + 13 + 9}{2} =$18

$\text{Area} = \sqrt{18 \left(18 - 14\right) \left(18 - 13\right) \left(18 - 9\right)}$

 \ \ \ \ \ \ \ \ \ =sqrt(18(4)(5)(9)

$\setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus = \sqrt{3240} = 18 \sqrt{10}$ square units