To find the surface area of the two-tiered steps, we need to calculate the surface area of each rectangular prism separately and then add them together.
Surface area of large rectangular prism:
- Front and back faces: 17 inches * 6.5 inches * 2 = 221 inches squared
- Top and bottom faces: 17 inches * 8.5 inches * 2 = 289 inches squared
- Side faces: 6.5 inches * 8.5 inches * 2 = 110.5 inches squared
Total surface area of large rectangular prism: 221 + 289 + 110.5 = 620.5 inches squared
Surface area of small rectangular prism:
- Front and back faces: 14 inches * 6.5 inches * 2 = 182 inches squared
- Top and bottom faces: 8.5 inches * 14 inches * 2 = 238 inches squared
- Side faces: 6.5 inches * 8.5 inches * 2 = 110.5 inches squared
Total surface area of small rectangular prism: 182 + 238 + 110.5 = 530.5 inches squared
Total surface area of two-tiered steps: 620.5 + 530.5 = 1151 inches squared
Therefore, the correct answer is 1,171.5 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
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
1,409.5 in. squared
879 in.2
879 in. squared
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