Question

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

Answer 1

≈ 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 `= (a+b+c)/2 = (9+5+11)/2 = 25/2 = 12.5`

step 2 : `A = sqrt(s(s-a)(s-b)(s-c))`

`= sqrt(12.5(12.5-9)(12.5-5)(12.5-11))`

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