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
330 cm2
330 cm squared
287 cm2
287 cm squared
810 cm2
810 cm squared
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To find the surface area of the triangular prism (cheese wedge), we need to find the area of each of the faces and add them together.
There are 2 triangular faces and 3 rectangular faces on a triangular prism. The formula to find the surface area of a triangular prism is:
Surface Area = 2(base area) + (perimeter of base x height)
Given that the base is a right triangle with base 9 cm, height 5 cm, and hypotenuse 13 cm, we can calculate the area of the base using the area formula for a triangle (1/2 x base x height)
Area of base = 1/2 x 9 x 5 = 22.5 cm²
Similarly, the perimeter of the triangle base is given by the sum of all three sides:
Perimeter = 9 + 5 + 13 = 27 cm
Now, we can calculate the surface area:
Surface Area = 2(22.5) + 27 x 12
Surface Area = 45 + 324
Surface Area = 369 cm²
Therefore, 369 cm² of plastic wrap is needed to cover the wedge of cheese.
None of the options given matches the calculated surface area, so the closest option would be 330 cm².