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
240 cm2
240 cm squared
287 cm2
287 cm squared
810 cm2
810 cm squared
330 cm2
330 cm squared
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To calculate the surface area of the triangular prism (which is the amount of plastic wrap needed to cover it), we need to find the area of each individual face and then add them all together.
The triangular face has an area of 1/2 * base * height, which in this case is 1/2 * 9 * 5 = 22.5 cm^2 * 2 (since there are two triangular faces) = 45 cm^2.
The rectangular faces each have an area of length * width, which in this case is 9 * 12 = 108 cm^2 * 3 (since there are three rectangular faces) = 324 cm^2.
Now, add the areas of the triangular faces and the rectangular faces together:
45 cm^2 (triangular faces) + 324 cm^2 (rectangular faces) = 369 cm^2.
Therefore, the amount of plastic wrap needed to cover the wedge of cheese is 369 cm^2.