# How do you use Heron's formula to determine the area of a triangle with sides of that are 14, 9, and 13 units in length?

Jan 23, 2016

$18 \sqrt{10} s q . u n i t s$

#### Explanation:

Use Heron's formula:-
sqrt(s(s-a)(s-b)(s-c) Where $S = \frac{a + b + c}{2}$

So
$a = 14 , b = 9 , c = 13 , S = 18 =$ $\frac{9 + 13 + 14}{2}$

$\rightarrow \sqrt{18 \left(18 - 14\right) \left(18 - 13\right) \left(18 - 9\right)}$

$\rightarrow \sqrt{18 \left(4\right) \left(5\right) \left(9\right)}$

$\rightarrow \sqrt{18 \left(180\right)}$

$\rightarrow \sqrt{3240}$

$\sqrt{3240} = 18 \sqrt{10}$