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?
To find the surface area of the triangular prism (which represents the amount of plastic wrap needed), we need to find the area of all the faces and add them up.
First, find the area of the triangular face:
1/2 * base * height
= 1/2 * 9 * 5
= 22.5 square centimeters
Then, find the area of the other two rectangular faces:
Base * height
= 12 * 5
= 60 square centimeters
Since there are two rectangular faces, multiply by 2:
60 * 2 = 120 square centimeters
Add the area of the triangular face to the area of the rectangular faces:
22.5 + 120 = 142.5 square centimeters
Therefore, 142.5 square centimeters of plastic wrap is needed to cover the wedge of cheese.