Emily is using glass to make a display case in the shape of a triangular prism. The net of the display case is shown.



Question
Exactly how much glass is needed to make the display case?

Answer options with 5 options
A.
82 feet squared

B.
104 feet squared

C.
120 feet squared

D.
168 feet squared

E.
180 feet squared

1 answer

To find the total amount of glass needed to make the display case, we need to find the surface area of the net.

The net consists of 2 triangular faces and 3 rectangular faces.

To find the area of a triangle, we use the formula A = (base x height) / 2.

For one triangle, we have a base of 12 feet and a height of 8 feet. So the area of one triangle is (12 x 8) / 2 = 48 feet squared.

There are 2 triangular faces, so the total area of the triangular faces is 2 x 48 = 96 feet squared.

For the rectangular faces, we have a length of 12 feet and a height of 6 feet for two of them, and a length of 8 feet and a height of 6 feet for the other one.

So the area of the first rectangular face is 12 x 6 = 72 feet squared, and the area of the second rectangular face is also 72 feet squared.

The third rectangular face has an area of 8 x 6 = 48 feet squared.

The total area of the rectangular faces is 72 + 72 + 48 = 192 feet squared.

Therefore, the total amount of glass needed to make the display case is 96 + 192 = <<96+192=288>>288 feet squared.

None of the answer options provided match the correct answer.