Surface Area Unit Test
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Question
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
816 cm squared
960 cm2
960 cm squared
720 cm2
720 cm squared
1,056 cm2
1,056 cm squared
First, we need to calculate the total surface area of the triangular prism.
The lateral surface area of a triangular prism can be calculated by finding the perimeter of the base triangle and then multiplying it by the height of the prism. Since the base triangle is an isosceles triangle, its sides are all 20 cm each. Therefore, the perimeter is 20 + 20 + 20 = 60 cm.
The height of the prism is the same as the height of the rectangles, which is 16 cm.
The lateral surface area of the prism is 60 cm * 16 cm = 960 cm².
The area of the top and bottom faces (rectangles) can be calculated by finding the area of one rectangle and then multiplying it by 2. The area of one rectangle is 20 cm * 20 cm = 400 cm². Therefore, the total area of the top and bottom faces is 400 cm² * 2 = 800 cm².
Therefore, the total surface area of the prism is 960 cm² (lateral surface area) + 800 cm² (top and bottom faces) = 1,760 cm².
Since the faces are covered in red foil, we need to calculate the lateral surface area for the red foil. This is the same as the lateral surface area of the prism, which is 960 cm².
Therefore, the amount of red foil needed for one candy bar is 960 cm².
So, the correct answer is:
960 cm2
960 cm squared