Question

What is the surface area of the triangular prism?

Answer 1

check the picture below.

so the prism is really two triangles, front and back, and three rectangles, stacked up to each other at the edges.

now, if we just get the area of each of those figures, and sum them up, that's the area of the triangular prism.

the triangles have a height of 9, a base of 24, recall A = (1/2)bh.

left and right rectangles are just 40x15.

the rectangles at the base is just 40x24

`\bf \stackrel{\textit{2 triangles}}{2\left[ \cfrac{1}{2}(24)(9) \right]}~~+~~\stackrel{\textit{left and right rectangles}}{2(40\cdot 15)}~~+~~\stackrel{\textit{base triangle}}{(40\cdot 24)} \\\\\\ 216+1200+960\implies 2376`

Answer 2

2376 ft^2

Explanation:

The surface area consists of 2 triangles of equal area + 2 rectangles of equal are + 1 other rectangle (the base)

= 2 * 1/2 * 9 * 24 + 2 * 15 * 40 + 24 * 40

= 2376 ft^2