Question

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 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

Answer 1

To find the surface area of the rectangular prism, we need to calculate the area of all six rectangles that make up its surface.

From the information given:

1. The area of the second rectangle (smaller) is 24 square inches.
2. The area of the top rectangle (first larger rectangle) is 54 square inches.
3. The area of the third rectangle (the second larger rectangle) is 36 square inches.
4. The fourth rectangle (smaller) is similar to the second and also has an area of 24 square inches.

Since there are two smaller rectangles (first and fourth) with areas of 24 square inches each, and the two larger rectangles (first and third) with areas of 54 and 36 square inches respectively, we sum these areas to find the total surface area.

The surface area of the rectangular prism is calculated as follows:

\[ \text{Surface Area} = 2(\text{Area of Rectangle 1} + \text{Area of Rectangle 2} + \text{Area of Rectangle 3}) \]

Plugging in the values:

\[ \text{Surface Area} = 2(54 + 24 + 36) \] \[ = 2(114) \] \[ = 228 \]

Thus, the surface area of the rectangular prism is \( \boxed{228} \) square inches.