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
810 cm2
810 cm squared
287 cm2
To find the surface area of the triangular prism, we need to calculate the area of each face.
1. The area of the triangular face is 1/2 * base * height = 1/2 * 9 * 5 = 22.5 cm^2
2. There are 2 triangular faces, so the total area of both triangular faces is 2 * 22.5 = 45 cm^2
3. The area of the rectangular face is length * width = 12 * 5 = 60 cm^2
4. There are 2 rectangular faces, so the total area of both rectangular faces is 2 * 60 = 120 cm^2
Adding both the areas of the triangular and rectangular faces, we get: 45 + 120 = 165 cm^2
Since the plastic wrap needs to cover all the faces of the triangular prism, the total area required is 165 cm^2. Therefore, the correct answer is 165 cm^2.