# A triangle has sides with lengths: 7, 2, and 8. How do you find the area of the triangle using Heron's formula?

Mar 26, 2018

$\approx 6.437 \text{ to 3 dec. places}$

#### Explanation:

$\text{Heron's formula is in 2 parts}$

• " calculate the semi-perimeter (s)"

$s = \frac{a + b + c}{2}$

$\text{where a, b and c are the sides of the triangle}$

$\text{let "a=7, b=2" and } c = 8$

$\Rightarrow s = \frac{7 + 2 + 8}{2} = \frac{17}{2}$

• " calculate the area (A) using the formula"

$A = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

$\textcolor{w h i t e}{A} = \sqrt{\frac{17}{2} \left(\frac{17}{2} - 7\right) \left(\frac{17}{2} - 2\right) \left(\frac{17}{2} - 8\right)}$

$\textcolor{w h i t e}{A} = \sqrt{\frac{17}{2} \left(\frac{3}{2}\right) \left(\frac{13}{2}\right) \left(\frac{1}{2}\right)}$

$\textcolor{w h i t e}{A} = \sqrt{\frac{663}{16}} \approx 6.437$