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
816 cm2
960 cm2
1,056 cm2
720 cm2
To calculate the total surface area of the triangular prism, we need to find the area of each face and add them together.
Each horizontal rectangle has an area of 20 cm * 16 cm = 320 cm^2. There are 3 of these rectangles, so the total area covered in gold foil is 3 * 320 cm^2 = 960 cm^2.
Each triangle has an area of (1/2) * base * height = (1/2) * 20 cm * 6 cm = 60 cm^2. There are 2 triangles, so the total area of the triangles is 2 * 60 cm^2 = 120 cm^2.
Therefore, the total area of red foil needed for one candy bar is 960 cm^2 + 120 cm^2 = 1,080 cm^2.
The closest option is 1,056 cm^2.
is this correct?
Apologies for the mistake in my previous response. Let's recalculate:
Each horizontal rectangle has an area of 20 cm * 16 cm = 320 cm^2. There are 3 of these rectangles, so the total area covered in gold foil is 3 * 320 cm^2 = 960 cm^2.
Each triangle has an area of (1/2) * base * height = (1/2) * 20 cm * 6 cm = 60 cm^2. There are 2 triangles, so the total area of the triangles is 2 * 60 cm^2 = 120 cm^2.
Therefore, the total area of red foil needed for one candy bar is 960 cm^2 (horizontal rectangles) + 120 cm^2 (triangles) = 1,080 cm^2.
The correct answer for the area of red foil needed for one candy bar is 1,080 cm^2, which is not one of the options provided. So, if we round to the closest option, the best choice would be 1,056 cm^2. Thank you for pointing out the mistake.