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 up.
1. First small rectangle: Let the dimensions be x and y.
2. Second larger rectangle: Let the dimensions be 5 cm and 9 cm (bottom and right side).
3. Third small rectangle: Same dimensions as the first small rectangle.
4. Fourth larger rectangle: Let the dimensions be 5 cm and 8 cm.
5. Fifth rectangle: 9 cm and 8 cm (shared side with the fourth larger rectangle).
6. Sixth rectangle: 9 cm and x (shared side with the first small rectangle).
Adding up the areas of each rectangle:
1. (x)(y)
2. 5(9)
3. (x)(y)
4. 5(8)
5. 9(8)
6. 9(x)
Surface area = (x)(y) + 5(9) + (x)(y) + 5(8) + 9(8) + 9(x)
Surface area = 2xy + 45 + 40 + 72 + 9x
Surface area = 2xy + 157 + 9x
Without knowing the values of the dimensions x and y, we cannot calculate the exact surface area.
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 smaller. The second and fourth are similar and bigger. The first rectangle is unlabeled. The second rectangle shares the top and bottom sides with two similar rectangles, one on each side. The top rectangle is labeled as 9 centimeters on the bottom and 5 centimeters on the right side. The right most rectangle is labeled 8 cm vertically on the right side.
What is the surface area of the rectangular prism?(1 point)
___cm2
5 answers
Yes. You. Can!
I apologize for the oversight. Let's calculate the surface area:
Given dimensions:
- First small rectangle: x by y
- Second larger rectangle: 5 cm by 9 cm
- Third small rectangle: x by y
- Fourth larger rectangle: 5 cm by 8 cm
- Fifth rectangle: 9 cm by 8 cm
- Sixth rectangle: 9 cm by x
Surface area = 2xy + 45 + 2xy + 40 + 72 + 9x
Surface area = 4xy + 157 + 9x
So, the surface area of the rectangular prism is 4xy + 157 + 9x cm^2.
Given dimensions:
- First small rectangle: x by y
- Second larger rectangle: 5 cm by 9 cm
- Third small rectangle: x by y
- Fourth larger rectangle: 5 cm by 8 cm
- Fifth rectangle: 9 cm by 8 cm
- Sixth rectangle: 9 cm by x
Surface area = 2xy + 45 + 2xy + 40 + 72 + 9x
Surface area = 4xy + 157 + 9x
So, the surface area of the rectangular prism is 4xy + 157 + 9x cm^2.
no
Apologies for the mistake. Let's correct the calculation to find the surface area of the rectangular prism:
Surface area = (2xy + 45) + (2xy + 40) + (72 + 9x)
Surface area = 4xy + 85 + 9x + 72
Surface area = 4xy + 9x + 157
Therefore, the surface area of the rectangular prism is 4xy + 9x + 157 cm^2.
Surface area = (2xy + 45) + (2xy + 40) + (72 + 9x)
Surface area = 4xy + 85 + 9x + 72
Surface area = 4xy + 9x + 157
Therefore, the surface area of the rectangular prism is 4xy + 9x + 157 cm^2.