Use the image to answer the question.

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
give it to me

Answer 1

To find the surface area of the rectangular prism, we need to determine the areas of all six rectangular faces, which consist of:

• Two big rectangles (the first and the third rectangles).
• Two small rectangles (the second and the fourth rectangles).
• Two additional rectangles on the sides (which are similar to the first and third).

From the information given:

1. Area of the second rectangle (small) = 24 square inches
2. Area of the fourth rectangle (small, similar to the second) = 24 square inches
3. Area of the first rectangle (big) = 54 square inches
4. Area of the third rectangle (big, similar to the first) = 36 square inches

Now, we can calculate the surface area:

• Surface area = 2*(Area of first rectangle + Area of second rectangle + Area of third rectangle + Area of fourth rectangle)

Calculating:

Big rectangles area: \(54 + 36 = 90\) square inches (total area of first and third) Small rectangles area: \(24 + 24 = 48\) square inches (total area of second and fourth)

Now, combine these:

Total area = \(90 + 48 = 138\) square inches

Finally, we multiply by 2 (for opposite sides):

Surface area = \(2 \times 138 = 276\) square inches.

So, the surface area of the rectangular prism is 276 square inches.