# How do you use Heron's formula to find the area of a triangle with sides of lengths 9 , 5 , and 11 ?

Mar 15, 2016

≈ 22.185

#### Explanation:

This is a two step process

step 1 : Find half the perimeter (s) of the triangle

step 2 : calculate the area (A)

let a = 9 , b = 5 and c = 11

step 1 : s $= \frac{a + b + c}{2} = \frac{9 + 5 + 11}{2} = \frac{25}{2} = 12.5$

step 2 : $A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

$= \sqrt{12.5 \left(12.5 - 9\right) \left(12.5 - 5\right) \left(12.5 - 11\right)}$

rArr A = sqrt(12.5xx3.5xx7.5xx1.5) ≈ 22.185