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
16
5* 16=80cm^2
Left Side
13
16
13* 16=208cm^2
Right Side
12
16
12* 16=192cm^2
Now let's take a look at the triangles. Notice that the bases 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 30 square centimeters. Since the triangles are congruent, the area of each triangle is 30 square centimeters. Now we have all the information that we need to find the total surface area of the triangular prism.
Total Surface Area
80+ 208+ 192+ 30+ 30=540cm^2
The total surface area of the triangular prism is 540 square centimeters.
