Question

What is the height of the triangular prism if the Surface Area is 180 inches squared

Answer 1

just a quick addition to "jsimpson11000" posting above

keeping in mind that for a triangular prism, the base is always the triangular face.

Check the picture below.

`5h~~ + ~~12h~~ + ~~\stackrel{\textit{two triangles}}{2\left[\cfrac{1}{2}(12)(5) \right]}~~ + ~~13h~~ = ~~180 \\\\\\ 60+30h=180\implies 30(2+h)=180\implies 2+h=\cfrac{180}{30} \\\\\\ 2+h=6\implies \boxed{h=4}`

Answer 2

4 in

Explanation:

Surface area = 1/2 ( 5x12) *2 + 5 x h + 13 * h + 12 x h

60 + 30h = 180

h = 4 in