Question

Find the surface area of the solid. Round to two decimal places

Answer 1

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.

$\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{34^2-22^2}=b\implies \sqrt{672}=b$

so then the surface area of the triangular prism is,

$\bf \stackrel{\textit{left and right}}{2(34\cdot 76)}~~+~~\stackrel{\textit{bottom}}{(44\cdot 76)}~~+~~\stackrel{\textit{front and back}}{2\left[\cfrac{1}{2}(44)(\sqrt{672}) \right]} \\\\\\ 8512~~+~~(44)(\sqrt{672})\qquad \approx\qquad 9652.61036291978$