Applications of Surface Area of Prisms Quick Check
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Question
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
240 cm squared
287 cm2
287 cm squared
330 cm2
330 cm squared
810 cm2
810 cm squared
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To find the amount of plastic wrap needed to cover the wedge of cheese, we need to calculate the surface area of the prism.
The surface area of a triangular prism can be calculated using the formula:
SA = 2bh + lw + lh
where
b = base of the triangle (in this case 9 cm)
h = height of the triangle (in this case 5 cm)
l = length of the prism (in this case 12 cm)
w = width of the prism (in this case also 12 cm)
Plugging in the values, we get:
SA = 2(9)(5) + (12)(12) + (12)(5)
SA = 90 + 144 + 60
SA = 294 cm2
Therefore, the correct answer is: 287 cm2
?
I apologize for the mistake in my previous response.
To find the amount of plastic wrap needed to cover the wedge of cheese, we can calculate the surface area of the triangular prism.
The surface area of a triangular prism can be calculated using the formula:
SA = 2 * base * height of triangle + base of triangle * length of prism + perimeter of triangle * height of prism
Given the dimensions of the triangular prism:
Base of triangle = 9 cm
Height of triangle = 5 cm
Length of prism = 12 cm
Height of prism = 12 cm (as it is a right triangular prism, the height of the prism is the hypotenuse of the triangle)
Plugging in the values into the formula, we get:
SA = 2 * 9 * 5 + 9 * 12 + 33.6
SA = 90 + 108 + 33.6
SA = 231.6 cm^2
Therefore, the amount of plastic wrap needed to cover the wedge of cheese is approximately 231.6 cm^2. The closest answer choice is 240 cm^2.
9 is the lenght not base
I apologize for the error. Let's correct the calculation using the correct values:
Given the dimensions of the triangular prism:
Base of triangle = 12 cm
Height of triangle = 5 cm
Length of prism = 12 cm (height of the prism, as you mentioned)
Plugging in the values into the formula, we get:
SA = 2 * 12 * 5 + 12 * 12 + 52.8
SA = 120 + 144 + 52.8
SA = 316.8 cm^2
Therefore, the amount of plastic wrap needed to cover the wedge of cheese is approximately 316.8 cm^2. The closest answer choice is 330 cm^2.