Applications of Surface Area of Prisms Quick Check
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Question
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
810 cm2
810 cm squared
287 cm2
287 cm squared
240 cm2
240 cm squared
330 cm2
330 cm squared
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To find the surface area of the triangular prism (wedge of cheese), you need to calculate the area of each face and add them together.
The triangular face has dimensions 9 cm (base) and 5 cm (perpendicular side), so its area is 0.5 * 9 * 5 = 22.5 cm^2.
There are two triangular faces on the prism, so the total area of the triangular faces is 2 * 22.5 = 45 cm^2.
The rectangular faces of the prism have dimensions 12 cm (length) and 9 cm (height), so each face has an area of 12 * 9 = 108 cm^2.
There are three rectangular faces on the prism, so the total area of the rectangular faces is 3 * 108 = 324 cm^2.
Adding the areas of the triangular and rectangular faces together, the total surface area of the prism is 45 + 324 = 369 cm^2.
Therefore, you will need 369 cm^2 of plastic wrap to cover the wedge of cheese.
Answer: 369 cm2