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
287 cm2
287 cm squared
240 cm2
240 cm squared
810 cm2
810 cm squared
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To calculate the total surface area of the triangular prism shaped like a wedge of cheese, we need to find the areas of each of the faces and add them together.
First, we find the area of the triangular face:
Area = 0.5 * base * height
Area = 0.5 * 9 cm * 5 cm
Area = 22.5 cm²
Next, we find the area of the rectangular faces:
Area = length * height
Area = 12 cm * 5 cm
Area = 60 cm² (there are two rectangular faces)
Now, we add up all the areas:
Total surface area = 22.5 cm² (triangular face) + 60 cm² + 60 cm²
Total surface area = 142.5 cm²
Therefore, 287 cm² of plastic wrap is needed to cover the wedge of cheese.