To find the surface area of the two-tiered steps, you need to calculate the surface area of both the large and small rectangular prisms separately and then add them together.
Surface area of the large prism:
- Front and back faces: 17 inches x 6.5 inches = 110.5 in^2 x 2 = 221 in^2
- Top and bottom faces: 17 inches x 8.5 inches = 144.5 in^2 x 2 = 289 in^2
- Side faces: 6.5 inches x 8.5 inches = 55.25 in^2 x 2 = 110.5 in^2
Total surface area of the large prism = 221 in^2 + 289 in^2 + 110.5 in^2 = 620.5 in^2
Surface area of the small prism:
- Front face: 14 inches x 6.5 inches = 91 in^2
- Top face: 14 inches x 8.5 inches = 119 in^2
- Side faces (hidden): 6.5 inches x 8.5 inches = 55.25 in^2
Total surface area of the small prism = 91 in^2 + 119 in^2 = 210 in^2
Overall surface area of the two-tiered steps = 620.5 in^2 + 210 in^2 = 830.5 in^2
Therefore, the correct response is: 830.5 in^2
Use the image to answer the question.
An illustration shows a small rectangular prism placed on top of a large rectangular prism, to form a 2-tiered step. The edges that are not visible are marked with dashed lines. The length of the large rectangular prism on the bottom is 17 inches and the height is 6.5 inches. The small rectangular prism placed on top along the back edge shows a width of 14 inches, which aligns with the width of the bottom rectangular prism. The total height of both rectangles is 13 inches overall. The length of the large rectangular prism that is not covered by the small rectangular prism is 8.5 inches.
Find the surface area of the two-tiered steps.
(1 point)
Responses
879 in.2
879 in. squared
1,171.5 in.2
1,171.5 in. squared
2,320.5 in.2
2,320.5 in. squared
1,409.5 in.2
3 answers
one
The correct answer is 879 in^2. Thank you for pointing out the error in my previous response.
4 answers