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 third rectangle is labeled 4 inches on the top horizontally. The fourth rectangle is labeled as 2.25 inches on the top and 8 inches on the right side. The first 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)
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To find the surface area of the rectangular prism, we need to find the area of each of the 6 rectangles and then add them all up.
Let's label the rectangles:
1. 4 inches x x inches (unlabeled)
2. 2.25 inches x 4 inches
3. 4 inches x 8 inches
4. 2.25 inches x 8 inches
5. 4 inches x x inches (unlabeled)
6. 4 inches x x inches (unlabeled)
1. Area of the first rectangle: 4 inches * 4 inches = 16 square inches
2. Area of the second rectangle: 2.25 inches * 4 inches = 9 square inches
3. Area of the third rectangle: 4 inches * 8 inches = 32 square inches
4. Area of the fourth rectangle: 2.25 inches * 8 inches = 18 square inches
Adding them all up:
16 + 9 + 32 + 18 = 75 square inches
Therefore, the surface area of the rectangular prism is 75 square inches.
nope
Let's try to find the correct answer:
1. The total surface area of a rectangular prism is the sum of the areas of all six faces.
2. The rectangular prism has 3 pairs of opposite faces with the same dimensions.
3. Let's calculate the area of each face:
- Face 1 and Face 2 (top and bottom): 4 inches * 8 inches = 32 square inches each
- Face 3 and Face 4 (sides): 4 inches * 4 inches = 16 square inches each
- Face 5 and Face 6 (front and back): 8 inches * 4 inches = 32 square inches each
4. Now, add up the areas of all six faces:
32 + 32 + 16 + 16 + 32 + 32 = 160 square inches
Therefore, the surface area of the rectangular prism is 160 square inches.
no
Let's try to find the correct answer again:
To find the surface area of the rectangular prism, we need to calculate the area of each of the six faces and then add them together.
Given information:
- Face 1 (4 inches x x inches)
- Face 2 (2.25 inches x 4 inches)
- Face 3 (4 inches x 8 inches)
- Face 4 (2.25 inches x 8 inches)
- Face 5 (4 inches x x inches)
- Face 6 (4 inches x x inches)
Calculations:
1. Face 1: 4 inches * x inches (unlabeled)
2. Face 2: 2.25 inches * 4 inches = 9 square inches
3. Face 3: 4 inches * 8 inches = 32 square inches
4. Face 4: 2.25 inches * 8 inches = 18 square inches
5. Face 5: 4 inches * x inches (unlabeled)
6. Face 6: 4 inches * x inches (unlabeled)
The total surface area would be the sum of the areas of each face:
Surface area = Face 1 + Face 2 + Face 3 + Face 4 + Face 5 + Face 6
Surface area = x * 4 + 9 + 32 + 18 + x * 4 + x * 4
Surface area = 8x + 9 + 32 + 18 + 8 + 4x
Surface area = 12x + 67 square inches
Therefore, the surface area of the rectangular prism is 12x + 67 square inches.
Wrong
Apologies for the errors in the previous attempts. Let's calculate the surface area of the rectangular prism accurately this time.
Given information:
- face 1: 4 inches x x inches
- face 2: 2.25 inches x 4 inches
- face 3: 4 inches x 8 inches
- face 4: 2.25 inches x 8 inches
- face 5: 4 inches x x inches
- face 6: 4 inches x x inches
Calculating the surface area:
1. Face 1 area: 4 inches * x inches = 4x square inches
2. Face 2 area: 2.25 inches * 4 inches = 9 square inches
3. Face 3 area: 4 inches * 8 inches = 32 square inches
4. Face 4 area: 2.25 inches * 8 inches = 18 square inches
5. Face 5 area: 4 inches * x inches = 4x square inches
6. Face 6 area: 4 inches * x inches = 4x square inches
Adding the areas of all faces:
Total surface area = 4x + 9 + 32 + 18 + 4x + 4x
Total surface area = 12x + 63 square inches
Therefore, the surface area of the rectangular prism is 12x + 63 square inches. Thank you for your patience, and I hope this calculation is correct.
That is not right
Let's recalibrate our approach to calculating the surface area of the rectangular prism using the given information:
Given:
Face 1: 4 inches x x inches
Face 2: 2.25 inches x 4 inches
Face 3: 4 inches x 8 inches
Face 4: 2.25 inches x 8 inches
Face 5: 4 inches x x inches
Face 6: 4 inches x x inches
To find the total surface area of the rectangular prism, we need to calculate the area of each face and then sum them up.
Calculating the area of each face:
1. Face 1: 4 inches * x inches = 4x square inches
2. Face 2: 2.25 inches * 4 inches = 9 square inches
3. Face 3: 4 inches * 8 inches = 32 square inches
4. Face 4: 2.25 inches * 8 inches = 18 square inches
5. Face 5: 4 inches * x inches = 4x square inches
6. Face 6: 4 inches * x inches = 4x square inches
Total surface area:
Surface area = Face 1 + Face 2 + Face 3 + Face 4 + Face 5 + Face 6
Surface area = 4x + 9 + 32 + 18 + 4x + 4x
Surface area = 12x + 63 square inches
Therefore, the correct surface area of the rectangular prism is 12x + 63 square inches. Thank you for your patience.