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)
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To find the surface area of the rectangular prism, we need to calculate the area of each individual rectangle and then sum them up.
The bottom rectangle has an area of 24 square inches.
The top rectangle has an area of 54 square inches.
The third rectangle has an area of 36 square inches.
Since the top and bottom rectangles are similar, they have the same area. So, the total area of the top and bottom rectangles is 54 + 54 = 108 square inches.
The third rectangle shares two sides with the top and bottom rectangles, so we only need to count the areas of the remaining two sides. Thus, the total area of the third rectangle is 36 + 2(24) = 84 square inches.
The total surface area of the rectangular prism is the sum of all the individual rectangle areas: 24 + 108 + 84 = 216 square inches.
Therefore, the surface area of the rectangular prism is 216 square inches.