Question

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

Answer 1

≈ 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 = (a+b+c)/2 = (19+16+14)/2 = 24.5`

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

`A = sqrt(s(s-a)(s-b)(s-c))`

`= sqrt(24.5(24.5-19)(24.5-16)(24.5-14))`

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