Use the image to answer the question.
An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 9 centimeters. The perpendicular side of the triangular face measures 5 centimeters and the hypotenuse measures 13 centimeters.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
(1 point)
Responses
330 cm2
330 cm squared
810 cm2
810 cm squared
240 cm2
240 cm squared
287 cm2
287 cm squared
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page 13 of 13
To find the surface area of the triangular prism-shaped wedge of cheese, we need to find the area of all the faces that need to be covered by plastic wrap.
The total surface area can be found by adding the areas of the triangular face, the two rectangular faces, and the two parallelogram faces.
1. The area of the triangular face can be calculated using the formula 1/2 * base * height:
1/2 * 9 cm * 5 cm = 22.5 cm2
2. The area of the two rectangular faces can be calculated by finding the area of a rectangle using the formula length * width:
12 cm * 5 cm = 60 cm2 (for each face)
3. The area of the two parallelogram faces can be calculated by finding the area of a parallelogram using the formula base * height:
9 cm * 12 cm = 108 cm2 (for each face since they are congruent)
Now, add all the areas together:
22.5 cm2 (triangular face) + 60 cm2 (rectangular faces) + 60 cm2 (rectangular faces) + 108 cm2 (parallelogram faces) + 108 cm2 (parallelogram faces) = 358.5 cm2
Therefore, the amount of plastic wrap needed to cover the wedge of cheese is 358.5 cm2.
None of the given responses are a match, so the correct answer is not provided in the options.