How do you use Heron's formula to determine the area of a triangle with sides of that are 14, 8, and 13 units in length?

Feb 5, 2016

Area ≈ 51.17

Explanation:

Calculating the area is a 2 step process.

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

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

let a = 14 , b= 8 and c = 13

step 1 : $s = \frac{a + b + c}{2} = \frac{14 + 8 + 13}{2} = \frac{35}{2} = 17.5$

step 2 : A = sqrt(17.5(17.5-14)(17.5-8)(17.5-13)

 = sqrt(17.5 xx 3.5 xx 9.5 xx 4.5) ≈ 51.17 color(black)(" square units ")