# How do you use Heron's formula to find the area of a triangle with sides of lengths 7 , 5 , and 8 ?

Jan 25, 2016

$10 \sqrt{3}$ $s q . c {m}^{2}$

#### 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,$a = 7 , b = 5 , c = 8 , s = 10 = \frac{7 + 5 + 8}{2} = \frac{20}{2}$

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

$\rightarrow \sqrt{10 \left(10 - 7\right) \left(10 - 5\right) \left(10 - 8\right)}$

$\rightarrow \sqrt{10 \left(3\right) \left(5\right) \left(2\right)}$

$\rightarrow \sqrt{10 \left(30\right)}$

$\rightarrow \sqrt{300} = 10 \sqrt{3}$