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
287 cm2
287 cm squared
240 cm2
240 cm squared
810 cm2
To calculate the surface area of the triangular prism (wedge of cheese), we need to find the area of all the faces.
There are 2 triangular faces and 3 rectangular faces in a triangular prism. The area of a triangular face can be calculated using the formula (1/2) * base * height. Since we are given the base and height of the triangular face, we can plug in the values to find the area of one triangular face:
(1/2) * 9 cm * 5 cm = 22.5 cm²
Since there are 2 triangular faces, the total area of both triangular faces is:
2 * 22.5 cm² = 45 cm²
Now, let's calculate the area of the remaining 3 rectangular faces. The area of a rectangular face can be calculated using the formula length * height.
The length of the triangular prism is 12 cm and the height of the triangular faces is 5 cm.
There are 3 rectangular faces, so the total area is:
3 * 12 cm * 5 cm = 180 cm²
Now, we add up the areas of the triangular and rectangular faces:
45 cm² (triangular) + 180 cm (rectangular) = 225 cm²
Therefore, 225 cm² of plastic wrap is needed to cover the wedge of cheese.
sorry bot the answer was wrong it was 330
Apologies for the mistake in the calculation. Let's revisit the calculation:
The total surface area of a triangular prism can be calculated by finding the area of all the faces.
1) Triangular Faces:
The area of one triangular face is (1/2) * base * height.
For the triangular face given:
(1/2) * 9 cm * 5 cm = 22.5 cm²
Since there are 2 triangular faces, the total area of both triangular faces is:
2 * 22.5 cm² = 45 cm²
2) Rectangular Faces:
The area of a rectangular face is length * height.
For the rectangular faces, using the length as 12 cm and the height as 5 cm:
3 * 12 cm * 5 cm = 180 cm²
Now, add the areas of the triangular and rectangular faces:
45 cm² (triangular) + 180 cm² (rectangular) = 225 cm²
I realize now that the total surface area of the wedge of cheese, a triangular prism, is indeed 225 cm². Thank you for your understanding.
you just said the same thing
Apologies for repeating the same information. I understand that the correct answer based on your feedback is 330 cm². Thank you for pointing out the error.
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