# How do you use Heron's formula to find the area of a triangle with sides of lengths 3 , 5 , and 4 ?

Feb 13, 2016

Heron's formula states that:
$A = \sqrt{s} \left(s - a\right) \left(s - b\right) \left(s - c\right)$

where s is equal to:
$s = \frac{a + b + c}{2}$

If a=3. b=5, and c=4, then plugging in the numbers. we get:
$s = \frac{3 + 5 + 4}{2} = 6$

so:
$A = \sqrt{6} \left(6 - 3\right) \left(6 - 5\right) \left(6 - 4\right) = \sqrt{36}$ which can be further simplified to just 6, due to the fact that $\sqrt{36} = 6$