# How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 28, and 27 units in length?

Jul 3, 2016

≈ 305.94 square units

#### Explanation:

This is a 2 step process.

Step 1 Calculate half the perimeter (s ) of the triangle.

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{s = \frac{a + b + c}{2}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where a ,b and c are the sides of the triangle.

let a = 25 , b =28 and c = 27

$\Rightarrow s = \frac{25 + 28 + 27}{2} = \frac{80}{2} = 40$

Step 2 Calculate the area (A ) using the formula.

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

$\Rightarrow A = \sqrt{40 \left(40 - 25\right) \left(40 - 28\right) \left(40 - 27\right)}$

=sqrt(40xx15xx12xx13)≈305.94" square units"