Hey!
A triangular prism will always have 5 Faces (2 triangles, 3 rectangles). There are two ways to approach this problem: 1.) Intuitively and 2.) Formulaically.
1.) Intuitively!
We know that the area of a triangle is 1/2*b*h, where b is the base, and h is height. Calculate the area of both triangle bases using your given base and height, then add them together!
1/2*b*h + 1/2*b*h
or just b*h (since 1/2 + 1/2 = 1).
2 done, 3 to go.
Next, the area of a rectangle is l*w. The length is pretty easy to verify (always the length of the prism), but the width for two of these is actually the slant height of the triangles! We are told that the base was 6 feet, and that the other two sides were 5 ft. respectively. These three sides are your widths!
For your 3 faces, you'll have:
l*w1 + l*w2 + l*w3 = 8*5 + 8*5 + 8*6.
After adding all of these, you'll have your surface area value!
2.) Formulaically
Arguably easier, we could derive a formula that works for any triangular prism. All of the sides on a triangle can (theoretically) be different, so if we rewrote our sum of products, we would have:
SA = b*h + (side 1 + side 2 + side 3)*l
where b is the triangle base, h is the triangle height, and l is the length of the prism.
Let me know if you have questions!
