# A triangle has sides with lengths: 1, 5, and 8. How do you find the area of the triangle using Heron's formula?

Jan 2, 2016

$2 \sqrt{3} i$
This is an unsatisfactory result as it demonstrates that this triangle cannot exist.

#### Explanation:

Heron's formula states that the area of a triangle whose sides have lengths a, b, and c is:

$A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$
where s is the semiperimeter of the triangle; that is,

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

In this case; a = 1, b = 5, c = 8

Therefore $s = \frac{1 + 5 + 8}{2}$
$s = 7$

By Heron: $A = \sqrt{6.2 . - 1} = \sqrt{2.2 .3} i = 2 \sqrt{3} i$