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
240 cm2
240 cm squared
287 cm2
287 cm squared
810 cm2
810 cm squared
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To find the total surface area of the triangular prism-shaped wedge of cheese, we need to find the area of each face and add them up.
The triangular face has a base of 9 cm and a height of 5 cm, so the area of this face is (1/2) * base * height = (1/2) * 9 * 5 = 22.5 cm².
Since there are two triangular faces, the total area of the triangular faces is 2 * 22.5 = 45 cm².
The rectangle side of the prism has a length of 12 cm and a height of 5 cm, so the area of this face is length * height = 12 * 5 = 60 cm².
Since there are two rectangle faces, the total area of the rectangle faces is 2 * 60 = 120 cm².
Adding the areas of the triangular and rectangle faces, the total surface area of the triangular prism-shaped wedge of cheese is 45 + 120 = 165 cm².
Therefore, 165 cm² of plastic wrap is needed to cover the wedge of cheese.
choose from following
(1 point)
Responses
330 cm2
330 cm squared
240 cm2
240 cm squared
287 cm2
287 cm squared
810 cm2
810 cm squared
The correct response is:
240 cm2
240 cm squared