# How do you use Heron's formula to find the area of a triangle with sides of lengths 18 , 7 , and 13 ?

Jan 26, 2016

$6 \sqrt{38.} s q . c {m}^{2}$

#### Explanation:

Use Heron's formula:-
$\sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$
Where $s$=semi-perimeter of triangle=$\frac{a + b + c}{2}$

So,$a = 18 , b = 7 , c = 13 , s = 19 = \frac{18 + 7 + 13}{2} = \frac{38}{2}$

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

$\rightarrow \sqrt{19 \left(19 - 18\right) \left(19 - 7\right) \left(19 - 13\right)}$

$\rightarrow \sqrt{19 \left(1\right) \left(12\right) \left(6\right)}$

$\rightarrow \sqrt{19 \left(72\right)}$

$\rightarrow \sqrt{1368} = 6 \sqrt{38}$