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
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.