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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 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

35 ft.2
35 ft. squared

97 ft.2
97 ft. squared

168 ft.2
168 ft. squared

194 ft.2

Answer 1

To calculate the surface area of the rectangular prism, we can use the formula for the surface area of a rectangular prism, which is given by:

\[ \text{Surface Area} = 2(lw + lh + wh) \]

where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.

From the description, we have:

• The height \( h = 6 \) feet
• The width \( w = 8 \) feet
• The length \( l = 3.5 \) feet

Now, substituting these values into the surface area formula:

1. First, calculate the area of each pair of rectangles:

   • \( lw = 3.5 \times 8 = 28 \) ft²
   • \( lh = 3.5 \times 6 = 21 \) ft²
   • \( wh = 8 \times 6 = 48 \) ft²

2. Now sum these areas:

   \[ lw + lh + wh = 28 + 21 + 48 = 97 \]

3. Finally, multiply by 2 to find the total surface area:

   \[ \text{Surface Area} = 2 \times 97 = 194 \text{ ft²} \]

Thus, the surface area of the prism is 194 ft.².