# A triangle has sides with lengths: 2, 9, 10. How do you find the area of the triangle using Heron's formula?

Jun 27, 2016

≈ 8.182 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 3 sides of the triangle.

let a = 2 , b = 9 and c = 10

$\Rightarrow s = \frac{2 + 9 + 10}{2} = \frac{21}{2} = 10.5$

Step 2: Calculate the area (A ) using.

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

$A = \sqrt{10.5 \left(10.5 - 2\right) \left(10.5 - 9\right) \left(10.5 - 10\right)}$

=sqrt(10.5xx8.5xx1.5xx0.5)≈8.182" (3 dec. places) "