How do you use Heron's formula to find the area of a triangle with sides of lengths 19 , 16 , and 14 ?

Mar 16, 2016

≈ 109.665 square units

Explanation:

This is a two step process.

step 1 : calculate half the perimeter (s ) of the triangle.

let a = 19 , b = 16 and c = 14

$s = \frac{a + b + c}{2} = \frac{19 + 16 + 14}{2} = 24.5$

step 2 : calculate the area (A ) as follows :

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

$= \sqrt{24.5 \left(24.5 - 19\right) \left(24.5 - 16\right) \left(24.5 - 14\right)}$

 A = sqrt(24.5xx5.5xx8.5xx10.5) ≈ 109.665" square units "