# How do you use Heron's formula to determine the area of a triangle with sides of that are 12, 16, and 13 units in length?

Feb 9, 2016

Area ≈ 76.69

#### Explanation:

This is a 2 step process.

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

step 2 : calculate the area (A)

let a = 12 , b = 16 and c = 13

step 1 : $s = \frac{a + b + c}{2} = \frac{12 + 16 + 13}{2} = \frac{41}{2} = 20.5$

step 2 : calculate the area using

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

$= \sqrt{20.5 \left(20.5 - 12\right) \left(20.5 - 16\right) \left(20.5 - 13\right)}$

 = sqrt(20.5 xx8.5 xx4.5 xx7.5 ) =sqrt5880.9 ≈ 76.69