check the picture below.
so, to get the area of the triangles, we can simply run a perpendicular line from the top to the base, and end up with a right-triangle with a base of 22 and a hypotenuse of 34, let's find the altitude.
[tex]\bf \textit{using the pythagorean theorem}
\\\\
c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b
\qquad
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}
\\\\\\
\sqrt{34^2-22^2}=b\implies \sqrt{672}=b[/tex]
so then the surface area of the triangular prism is,
[tex]\bf \stackrel{\textit{left and right}}{2(34\cdot 76)}~~+~~\stackrel{\textit{bottom}}{(44\cdot 76)}~~+~~\stackrel{\textit{front and back}}{2\left[\cfrac{1}{2}(44)(\sqrt{672}) \right]}
\\\\\\
8512~~+~~(44)(\sqrt{672})\qquad \approx\qquad 9652.61036291978[/tex]
