How do you use Heron's formula to find the area of a triangle with sides of lengths 3 , 2 , and 4 ?

Feb 1, 2016

6.16185

Explanation:

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

$= \frac{3 + 2 + 4}{2}$

$= \frac{9}{2}$

$= 4.5$

from heron's law we know,

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

$= 4.5 \sqrt{\left(4.5 - 3\right) \left(4.5 - 2\right) \left(4.5 - 4\right)}$

$= 4.5 \sqrt{1.5 \times 2.5 \times 0.5}$

$= 4.5 \sqrt{1.875}$

$= 4.5 \times 1.3693$

$= 6.16185$