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Question

An illustration shows the unfolded version of a rectangular prism composed of 6 rectangles. There are four adjoining rectangles positioned horizontally. The first and third are similar and smaller. The top of the first rectangle is labeled 2 feet. The second and fourth are similar and bigger. The fourth rectangle is labeled 8 feet on the right side. The second rectangle shares the top and bottom sides with two similar rectangles, one on each side. The top rectangle is labeled as 5 feet on the top side.

Use this net to find the surface area of the rectangular prism it represents.

(1 point)
Responses

132 ft.2
132 ft squared

80 ft.2
80 ft squared

30 ft.2
30 ft squared

66 ft.2
66 ft squared
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Answer 1

To find the surface area of a rectangular prism, we need the dimensions of all six faces (rectangles) that make up the prism.

From the description, we have:

1. Smaller rectangles (two of them) with height 2 feet (let's denote their width as \( w_1 \)).
2. Larger rectangles (two of them) with height 8 feet (let's denote their width as \( w_2 \)).
3. The top rectangle has a length of 5 feet.

We need to find the width of the smaller rectangles to calculate the surface area.

Assuming that:

• The smaller rectangles with height 2 feet are in the front and back positions (like the sides) and are similar, and they share the same width \( w_1 \).
• The larger rectangles with height 8 feet are on the lateral sides and have the same width \( w_2 \).
• The top rectangle has a width equal to the combined total width of two smaller rectangles, meaning \( w_1 + w_1 + w_2 + w_2 = 5 , \text{ft} \).

If we assume:

• \( w_1 \) (smaller rectangle width) = \( 5/4 \) = 1.25 ft.
• \( w_2 \) (larger rectangle width) = \( 5/2 \) = 2.5 ft.

Now let's calculate the surface area using the formula: \[ \text{Surface Area} = 2lw + 2lh + 2wh \]

Given:

• Length \( = 5 , \text{ft} \),
• Height \( = 8 , \text{ft} \) for larger sides and \( = 2 , \text{ft} \) for smaller sides.

We find:

• Two smaller sides: \( 2(1.25 , \text{ft} \times 2 , \text{ft}) = 5 , \text{ft}^2 \)
• Two larger sides: \( 2(2.5 , \text{ft} \times 8 , \text{ft}) = 40 , \text{ft}^2 \)
• Top and bottom rectangle: \( 2(5 , \text{ft} \times 2.5 , \text{ft}) = 25 , \text{ft}^2 \)

Adding them together: \[ \text{Surface Area} = 5 + 40 + 25 = 70 , \text{ft}^2 \]

Given the calculations may not match the final options listed. Please check the arrangement and dimensions for correctness.

However, comparing with options:

• 132 ft.2
• 80 ft.2
• 30 ft.2
• 66 ft.2

The correct surface area using prospective calculations appears to be missing, suggesting potential re-evaluation is needed.

For surface area of \( 66 ft^2 \) is nearly close and might represent accurate dimensions given.

So, the closest answer would be: 66 ft.²