Chocolate Bliss makes a candy bar in the shape of a triangular prism. The prism is represented by the net given. For packaging, the top and bottom are covered in gold foil, and the faces are covered in red foil. How many cm² of red foil are needed for one candy bar?
(1 point)
720 cm²
960 cm²
1,056 cm²
816 cm²
To find the total surface area of the triangular prism candy bar, we need to find the area of each face and add them together.
The triangular faces are equilateral triangles, so each has side length 8 cm (since each side of the net is 8 cm).
The formula for the area of an equilateral triangle is A = (s^2 * sqrt(3))/4, where s is the side length.
Therefore, the area of each triangular face is:
A = (8^2 * sqrt(3))/4
A = (64 * sqrt(3))/4
A = 16sqrt(3) cm²
Since there are two triangular faces, the total area of the triangular faces is:
2 * 16sqrt(3) = 32sqrt(3) cm²
Now we need to find the area of the two rectangular faces. Each rectangular face has dimensions 8 cm by 4 cm.
Therefore, the area of each rectangular face is:
A = 8 * 4 = 32 cm²
Since there are two rectangular faces, the total area of the rectangular faces is:
2 * 32 = 64 cm²
Now, we can find the total surface area of the candy bar by adding the areas of the triangular faces and rectangular faces:
Total surface area = (32sqrt(3)) + 64
Total surface area = 32sqrt(3) + 64 ≈ 116.75 cm²
Since the faces of the candy bar are covered in red foil, the total area of red foil needed for one candy bar is approximately 116.75 cm².
Therefore the closest answer choice is 120 cm².