# How do you use Heron's formula to determine the area of a triangle with sides of that are 14, 7, and 13 units in length?

Feb 5, 2016

Area ≈ 45.17

#### Explanation:

Calculating the area is a 2 step process.

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

step 2 : calculate the area using

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

let a = 14 , b = 7 and c = 13

step 1 : $s = \frac{a + b + c}{2} = \frac{14 + 7 + 13}{2} = \frac{34}{2} = 17$

step 2 : $A = \sqrt{17 \left(17 - 14\right) \left(17 - 7\right) \left(17 - 13\right)}$

 = sqrt(17 xx 3 xx 10 xx 4) ≈ 45.17color(black)(" square units" )