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 measure 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 calculate the amount of plastic wrap needed to cover the wedge of cheese, we first need to find the surface area of the triangular prism.
The formula to calculate the surface area of a triangular prism is:
Surface Area = 2*(base*height) + base*length + height*length
In this case:
base = 9 cm
height = 5 cm
length = 12 cm
Substitute the values into the formula:
Surface Area = 2*(9*5) + 9*12 + 5*12
Surface Area = 2*(45) + 108 + 60
Surface Area = 90 + 108 + 60
Surface Area = 258 cm^2
Therefore, 258 square centimeters of plastic wrap are needed to cover the wedge of cheese.