The net is made up of rectangles and triangles. Let's calculate the area of each polygon separately, starting with the rectangles.
Rectangular Face
Length l
Width w
Area=l * w
Bottom
5
8
5* 8=40ft^2
Left Side
6.5
8
6.5* 8=52ft^2
Right Side
6.5
8
6.5* 8=52ft^2
Now let's take a look at the triangles. Note that the front and back of the prism are congruent triangles. This means that they have the same area. Let's substitute the measures of the front and back into the formula for the area of a triangle!
We found that the area of one triangle is 15 square feet. Since the triangles are congruent, that means that the area of both triangles is 15 square feet. Now we have all the information that we need to find the total surface area of the triangular prism.
Total Surface Area
40+ 52+ 52+ 15+ 15=174ft^2
The total surface area of the triangular prism is 174 square feet.
