The surface area of a rectangular prism is calculated by finding the area of each of the six faces and then adding them together.
In this case, the first and third rectangles have the same dimensions of 7 inches by 5 inches, for a total area of 35 square inches each (7 x 5 = 35).
The second rectangle has a dimension of 3 inches by 5 inches, for a total area of 15 square inches (3 x 5 = 15).
Since each face has a pair of identical faces, the total surface area is calculated by adding up all the areas:
2(35) + 2(15) + 2(35) = 70 + 30 + 70 = 170 square inches.
Therefore, the surface area of the rectangular prism is 170 square inches.
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 first rectangle is labeled 7 inches on the top horizontally. The second rectangle is labeled as 3 inches on the top and 5 inches vertically. The third rectangle shares the top and bottom sides with two similar rectangles, one on each side.
What is the surface area of the rectangular prism?(1 point)
in.2
5 answers
wrong
I apologize for the mistake. Let's recalculate the surface area of the rectangular prism with the correct dimensions.
The first rectangle has dimensions 7 inches by 5 inches, so its area is 7 x 5 = 35 square inches. There are two identical faces like this, so the total area is 2 x 35 = 70 square inches.
The second rectangle has dimensions 3 inches by 5 inches, so its area is 3 x 5 = 15 square inches. There are also two identical faces like this, so the total area is 2 x 15 = 30 square inches.
Finally, the third rectangle has dimensions 7 inches by 5 inches, so its area is also 35 square inches. There are two identical faces like this, so the total area is 2 x 35 = 70 square inches.
Adding up all the areas: 70 + 30 + 70 = 170 square inches.
Therefore, the correct surface area of the rectangular prism is 170 square inches. Thank you for your patience.
The first rectangle has dimensions 7 inches by 5 inches, so its area is 7 x 5 = 35 square inches. There are two identical faces like this, so the total area is 2 x 35 = 70 square inches.
The second rectangle has dimensions 3 inches by 5 inches, so its area is 3 x 5 = 15 square inches. There are also two identical faces like this, so the total area is 2 x 15 = 30 square inches.
Finally, the third rectangle has dimensions 7 inches by 5 inches, so its area is also 35 square inches. There are two identical faces like this, so the total area is 2 x 35 = 70 square inches.
Adding up all the areas: 70 + 30 + 70 = 170 square inches.
Therefore, the correct surface area of the rectangular prism is 170 square inches. Thank you for your patience.
still wrong
I apologize for the continued error. Let's take another approach.
The rectangular prism is composed of 6 faces:
- 2 faces with dimensions 7 inches by 5 inches (first and third rectangle)
- 2 faces with dimensions 3 inches by 5 inches (second and fourth rectangle)
- 2 faces with dimensions 7 inches by 3 inches (top and bottom)
Calculating the area of each face:
- 7 x 5 = 35 square inches (first and third rectangle)
- 3 x 5 = 15 square inches (second and fourth rectangle)
- 7 x 3 = 21 square inches (top and bottom)
Now, calculate the total surface area by adding the areas of all faces:
2(35) + 2(15) + 2(21) = 70 + 30 + 42 = 142 square inches.
Therefore, the correct surface area of the rectangular prism is 142 square inches. Thank you for your patience.
The rectangular prism is composed of 6 faces:
- 2 faces with dimensions 7 inches by 5 inches (first and third rectangle)
- 2 faces with dimensions 3 inches by 5 inches (second and fourth rectangle)
- 2 faces with dimensions 7 inches by 3 inches (top and bottom)
Calculating the area of each face:
- 7 x 5 = 35 square inches (first and third rectangle)
- 3 x 5 = 15 square inches (second and fourth rectangle)
- 7 x 3 = 21 square inches (top and bottom)
Now, calculate the total surface area by adding the areas of all faces:
2(35) + 2(15) + 2(21) = 70 + 30 + 42 = 142 square inches.
Therefore, the correct surface area of the rectangular prism is 142 square inches. Thank you for your patience.
11 answers