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
810 cm2
810 cm squared
287 cm2
287 cm squared
To calculate the surface area of the triangular prism shaped like a wedge of cheese, we need to find the area of each face and then add them all up.
1. The area of the triangular face can be calculated using the formula A = 1/2 * base * height. In this case, the base is 9 cm and the height is 5 cm.
A = 1/2 * 9 cm * 5 cm = 22.5 cm squared
2. The area of the rectangular face is given by length * height. In this case, the length is 12 cm and the height is 5 cm.
A = 12 cm * 5 cm = 60 cm squared
3. Since the triangular prism has two triangular faces and three rectangular faces, we need to take into account all of them to find the total surface area.
Total surface area = 2 * 22.5 cm squared (triangular faces) + 3 * 60 cm squared (rectangular faces)
Total surface area = 45 cm squared + 180 cm squared = 225 cm squared
Therefore, 225 cm squared of plastic wrap is needed to cover the wedge of cheese. The closest option to this answer is 240 cm squared.