I don't understand the question:

What is the area of an equilateral triangle with a side length of six feet on the surface?

Equilateral triangle = 60º + 60º + 60º

(1)
\begin{align} \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \ Sin(60^\circ) = \frac{height}{6} \end{align}

(2)
\begin{align} \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \ 6\times Sin(60^\circ) = height \end{align}

(3)
\begin{align} \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \ 6\frac{\surd{(3)}}{2} = height \end{align}

(4)
\begin{align} \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \ \frac{6\surd{(3)}}{2} = height \end{align}

(5)
\begin{align} \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \ \frac{3\surd{(3)}}{1} = height \end{align}

(6)
\begin{align} \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \ 3\surd{(3)} = height \end{align}

Height = 5.1962 (4dp)

(7)
\begin{align} \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \ Area\,of\,triangle = \frac{1}{2}\,base\times height \end{align}

(8)
\begin{align} \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \ Area\,of\,triangle = \frac{base\times height}{2} \end{align}

(9)
\begin{align} \definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \ Area\,of\,triangle = \frac{6\times 5.1962}{2} \end{align}

Area of triangle = 15.5885

I sincerely apologise for the ridiculous use of mathematical equations. I simply got excited and had a lot of fun (and obviously couldn't help myself be rational). LaTeX is fun!