Applications of Surface Area of Prisms Quick Check
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Question
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
287 cm2
287 cm squared
330 cm2
330 cm squared
240 cm2
240 cm squared
810 cm2
810 cm squared
To find the surface area of the wedge of cheese, you need to find the area of all five faces of the triangular prism.
First, find the area of the two triangular faces:
Area = 2 * (0.5 * base * height)
Area = 2 * (0.5 * 9 * 5)
Area = 2 * (0.5 * 45)
Area = 2 * 22.5
Area = 45 cm^2
Next, find the area of the three rectangular faces:
Area = 2lw + 2lh + 2wh
Area = 2(9)(12) + 2(12)(5) + 2(5)(9)
Area = 2(108) + 2(60) + 2(45)
Area = 216 + 120 + 90
Area = 426 cm^2
Finally, add the areas of all five faces together:
Total Surface Area = 45 + 426
Total Surface Area = 471 cm^2
Therefore, you would need 471 cm^2 of plastic wrap to cover the wedge of cheese.
None of the response options provided match the correct answer, so it seems there may be a miscalculation in the given choices.