Use the image to answer the question.
An illustration shows an unfolded version of a triangular prism.
There are 3 horizontal rectangles stacked on top of one another. The first and the last are similar and the middle one is larger. The horizontal length of the three rectangles is 20 centimeters. The vertical width of the second rectangle is 16 centimeters. There are two similar triangles adjoined to the left and right of the second rectangle, with the rectangle width as the triangle bases. The perpendicular length of the triangle, drawn as a dotted line from the top vertex to the middle of the base, is 6 centimeters; it is denoted by a right angle symbol. The length of the hypotenuse slant is 10 centimeters. All interior lines are drawn as dashed lines, and all outer lines are solid.
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)
Responses
1,056 cm2
1,056 cm squared
720 cm2
720 cm squared
960 cm2
960 cm squared
816 cm2
816 cm squared
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To find the total surface area of the triangular prism, we need to calculate the area of each face separately and then sum them up.
- The base and top rectangles have dimensions of 20 cm by 16 cm each. So each rectangle's area is 20 cm * 16 cm = 320 cm^2. Since there are 2 rectangles (top and bottom), the total area of the base and top is 320 cm^2 * 2 = 640 cm^2.
- The front and back faces are triangles with base 20 cm and height 6 cm. The area of each triangle is 1/2 * base * height = 1/2 * 20 cm * 6 cm = 60 cm^2. Since there are two triangles (front and back), the total area of the front and back faces is 60 cm^2 * 2 = 120 cm^2.
- The area of the larger middle rectangle is 20 cm * 16 cm = 320 cm^2.
Therefore, the total area of red foil needed for one candy bar is 640 cm^2 (base and top) + 120 cm^2 (front and back) + 320 cm^2 (middle) = 1080 cm^2.
So the correct answer is 1,080 cm^2, which is closest to 1,056 cm^2.