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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 bigger. The second and fourth are similar and smaller. The area of the second rectangle is labeled 24 square inches. The third rectangle shares the top and bottom sides with two similar rectangles, one on each side. The area of the top rectangle is labeled as 54 square inches and the area of the third rectangle is labeled as 36 square inches.

What is the surface area of the rectangular prism?

(1 point)
in.2
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Answer 1

To find the surface area of the rectangular prism, we need to sum the areas of all six rectangles that make up its surface. Based on the provided information:

1. Area of the first rectangle: Let this be \( A_1 \).
2. Area of the second rectangle: \( A_2 = 24 \) square inches.
3. Area of the third rectangle: \( A_3 = 36 \) square inches.
4. Area of the fourth rectangle: Let this be \( A_4 \).
5. Area of the fifth rectangle: \( A_5 = 54 \) square inches.
6. Area of the sixth rectangle: Let this be \( A_6 \).

From the information provided, we have:

• \( A_1 \) and \( A_3 \) are similar and bigger rectangles. Assuming \( A_1 = A_3 = 36 \) square inches.
• \( A_2 \) and \( A_4 \) are similar and smaller rectangles. Given \( A_2 = 24 \) square inches. Therefore, \( A_4 = A_2 = 24 \) square inches.
• \( A_5 = 54 \) square inches.

Now we can sum the areas of all rectangles:

\[ \text{Surface Area} = 2(A_1 + A_2 + A_3 + A_4 + A_5) \]

Substituting the areas we have:

\[ \text{Surface Area} = 2(36 + 24 + 36 + 24 + 54) \]

Calculating inside the parentheses:

\[ 36 + 24 + 36 + 24 + 54 = 174 \]

Now multiply by 2:

\[ \text{Surface Area} = 2 \times 174 = 348 \text{ square inches} \]

Thus, the surface area of the rectangular prism is 348 square inches.