# A triangle has sides with lengths: 4, 5, and 4. How do you find the area of the triangle using Heron's formula?

May 5, 2016

area ≈ 7.806 square units

#### Explanation:

This is a 2 step process.

Step 1

Calculate half the perimeter (s) of the triangle

let a = 4 , b = 5 and c = 4

$s = \frac{a + b + c}{2} = \frac{4 + 5 + 4}{2} = \frac{13}{2} = 6.5$

Step 2

Calculate the area (A) using

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$A = \sqrt{6.5 \left(6.5 - 4\right) \left(6.5 - 5\right) \left(6.5 - 4\right)}$

=sqrt(6.5xx2.5xx1.5xx2.5) ≈ 7.806" square units"