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
810 cm2
810 cm squared
240 cm2
240 cm squared
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To find the amount of plastic wrap needed to cover the wedge of cheese, we need to calculate the surface area of the triangular prism.
The formula for the surface area of a triangular prism is:
2( base x height of triangle) + ( perimeter of base x height of prism)
Given that the base of the triangular prism is a right triangle with a base of 9 cm and a height of 5 cm, the area of the triangle is:
(1/2)base x height = (1/2)(9)(5) = 22.5 cm squared
The perimeter of the base is the sum of all three sides of the triangle:
9 + 5 + 13 = 27 cm
Now, we can calculate the surface area of the triangular prism:
2(9 x 5) + (27 x 12) = 90 + 324 = 414 cm squared
Therefore, 414 cm squared of plastic wrap is needed to cover the wedge of cheese. None of the provided options match this result, so the most appropriate answer would be to skip the question or input 414 cm squared if given the option.