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
810 cm2
330 cm2
287 cm2
To find the surface area of the wedge of cheese, we must calculate the surface area of each individual face and then sum them up.
1. The triangular face with dimensions 12 cm, 9 cm, and 13 cm has an area of:
Area = 1/2 * base * height
Area = 1/2 * 12 * 9
Area = 1/2 * 108
Area = 54 cm2
2. There are two rectangular faces on the sides of the prism, each with dimensions 12 cm by 5 cm:
Area = length * width
Area = 12 * 5
Area = 60 cm2 (for each rectangular face)
Now add up the areas of all faces:
54 cm2 (triangular face) + 60 cm2 (rectangular face) + 60 cm2 (rectangular face) = 174 cm2
Therefore, the total surface area of the wedge of cheese is 174 cm2.
The closest answer choice is 240 cm2, which would be the total surface area if we included the bottom triangular face as well.
So, the correct answer is 240 cm2.