Question

Use the image to answer the question.

An illustration shows the unfolded version of a rectangular prism composed of 6 rectangles. There are four adjoining rectangles positioned vertically. The first and third are similar and bigger. The second and fourth are similar and smaller. The third rectangle is labeled as 6 feet on the left side. The fourth rectangle is labeled as 8 feet on the bottom side. The fourth rectangle shares the left and right sides with two similar rectangles, one on each side. The rectangle on the left is labeled as 3.5 feet on the left side.

What is the surface area of this prism?

(1 point)
Responses

168 ft.2
168 ft. squared

97 ft.2
97 ft. squared

194 ft.2
194 ft. squared

35 ft.2
35 ft. squared
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Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of the prism, we need to calculate the area of each of the 6 rectangles and then add them together.

1. The first rectangle (6 ft by 8 ft) has an area of 6 * 8 = 48 ft^2.
2. The second rectangle (6 ft by 3.5 ft) has an area of 6 * 3.5 = 21 ft^2.
3. The third rectangle (6 ft by 8 ft) has an area of 6 * 8 = 48 ft^2.
4. The fourth rectangle (8 ft by 3.5 ft) has an area of 8 * 3.5 = 28 ft^2.
5. The fifth rectangle (8 ft by 3.5 ft) has an area of 8 * 3.5 = 28 ft^2.
6. The sixth rectangle (6 ft by 3.5 ft) has an area of 6 * 3.5 = 21 ft^2.

Adding all the areas together:

48 + 21 + 48 + 28 + 28 + 21 = 194 ft^2

Therefore, the surface area of this prism is 194 ft^2.

Answer 2

Use the image to answer the question.

There are four adjoining rectangles of the same height positioned so their vertical sides touch. The first and third rectangles from the left are the same size as each other. The second and fourth rectangles from the left are also the same size as each other but wider than the first and third. The first rectangle is labeled 7 centimeters on the left side and 2 centimeters on the bottom side. The fourth rectangle is labeled 10 centimeters on the bottom side. The second rectangle has identical small rectangles touching its top and bottom sides. The small rectangles are the same width as the second rectangle.

The net of a rectangular prism is shown. What is the surface area of the rectangular prism?

(1 point)
Responses

138 cm.2
138 cm.2

306 cm.2
306 cm.2

104 cm.2
104 cm.2

208 cm.2
208 cm.2
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Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the surface area of the rectangular prism, we first need to calculate the areas of each face and then add them together.

Given the dimensions:
- The first rectangle: 7 cm x 2 cm = 14 cm^2
- The second rectangle (which is the same as the fourth rectangle): 10 cm x 2 cm = 20 cm^2
- The third rectangle (which is the same as the first rectangle): 7 cm x 2 cm = 14 cm^2
- The two small rectangles connecting the top and bottom of the second rectangle are both the same size as the second and fourth rectangle: 2 cm x 10 cm = 20 cm^2

Now we calculate the total surface area by adding all the areas together:
14 cm^2 + 20 cm^2 + 14 cm^2 + 20 cm^2 = 68 cm^2

Therefore, the surface area of the rectangular prism is 68 cm^2.

Answer 4

no

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the error in the previous calculation. Let's correct it:

Given the dimensions:
- The first rectangle: 7 cm x 2 cm = 14 cm^2
- The second rectangle (which is the same as the fourth rectangle): 10 cm x 2 cm = 20 cm^2
- The third rectangle (which is the same as the first rectangle): 7 cm x 2 cm = 14 cm^2
- The two small rectangles connecting the top and bottom of the second rectangle are both the same size as the second and fourth rectangle: 2 cm x 10 cm = 20 cm^2

Now we calculate the total surface area by adding all the areas together:
14 cm^2 + 20 cm^2 + 14 cm^2 + 20 cm^2 = 68 cm^2

However, this total only considers the area of the four sides (there are two of each) and the top and bottom faces. We also need to take into account the front and back faces of the prism.

The front and back faces have the dimensions of the first and second rectangles, which are 7 cm x 10 cm and 10 cm x 2 cm, respectively.

Area of the front face = 7 cm x 10 cm = 70 cm^2
Area of the back face = 10 cm x 2 cm = 20 cm^2

Now, we add all the areas together, including the front and back faces:
14 cm^2 + 20 cm^2 + 14 cm^2 + 20 cm^2 + 70 cm^2 + 20 cm^2 = 158 cm^2

Therefore, the correct surface area of the rectangular prism is 158 cm^2. Thank you for your patience and pointing out the mistake.