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 √(c^2-a^2)=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ √(34^2-22^2)=b\implies √(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)(√(672)) \right]} \\\\\\ 8512~~+~~(44)(√(672))\qquad \approx\qquad 9652.61036291978`