A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese 5 cm 9 cm 12 cm 13 cm
To calculate the amount of plastic wrap needed to cover the wedge of cheese, we need to find the surface area of all the faces of the triangular prism.
The formula for the surface area of a triangular prism is:
Surface area = (2 x base area) + (base perimeter x height)
First, let's calculate the base area of the triangle:
Base area = (1/2) x base x height
Base area = (1/2) x 5 cm x 9 cm
Base area = 22.5 cm²
Next, calculate the perimeter of the base triangle:
Base perimeter = 5 cm + 9 cm + 13 cm
Base perimeter = 27 cm
Now, we can find the surface area of all faces of the wedge of cheese:
Surface area = (2 x 22.5 cm²) + (27 cm x 12 cm)
Surface area = 45 cm² + 324 cm²
Surface area = 369 cm²
Therefore, to cover the wedge of cheese, 369 cm² of plastic wrap is needed.
Wrong that’s not one of the answer choices
A. 287 cm²
B. 330 cm²
C. 810 cm²
D. 240 cm²
My apologies for the error in the previous calculation. Let's correct it:
The total surface area of the wedge of cheese can be calculated as follows:
Surface area = (2 x base area) + (base perimeter x height)
First, we calculate the base area:
Base area = (1/2) x base x height
Base area = (1/2) x 5 cm x 9 cm = 22.5 cm²
Next, let's calculate the base perimeter:
Base perimeter = 5 cm + 9 cm + 13 cm = 27 cm
Now, we can find the total surface area of the wedge of cheese:
Surface area = (2 x 22.5 cm²) + (27 cm x 12 cm)
Surface area = 45 cm² + 324 cm²
Surface area = 369 cm²
Therefore, the correct answer for the amount of plastic wrap needed to cover the wedge of cheese is not listed in the given answer choices. This may be an error in the provided options.
All right, then, just get the closest answer
To determine the closest answer among the given choices, we can compare them to the calculated surface area of the wedge of cheese, which is 369 cm².
Among the given options:
A. 287 cm²
B. 330 cm²
C. 810 cm²
D. 240 cm²
The closest option to 369 cm² is option B, 330 cm². Although it is not an exact match, it is the closest one where we round the actual surface area of the wedge of cheese.