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
879 in.2
879 in. squared
1,409.5 in.2
1,409.5 in. squared
2,320.5 in.2
2,320.5 in. squared
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To find the surface area of both rectangular prisms, we first calculate the surface area of each prism separately and then add them together.
Surface area of the large rectangular prism:
- Front and back faces: 17 inches x 6.5 inches = 110.5 square inches for each
- Top and bottom faces: 17 inches x 8.5 inches = 144.5 square inches for each
- Side faces: 6.5 inches x 8.5 inches = 55.25 square inches for each (two of these)
Total surface area of the large rectangular prism = 2(110.5) + 2(144.5) + 2(55.25) = 221 + 289 + 110.5 = 620 square inches
Surface area of the small rectangular prism:
- Front and back faces: 14 inches x 6.5 inches = 91 square inches for each
- Side faces: 6.5 inches x 8.5 inches = 55.25 square inches for each (two of these)
- Top and bottom faces: 14 inches x 8.5 inches = 119 square inches for each
Total surface area of the small rectangular prism = 2(91) + 2(55.25) + 2(119) = 182 + 110.5 + 238 = 530.5 square inches
Total surface area of the two-tiered steps = Surface area of large rectangular prism + Surface area of small rectangular prism
Total surface area = 620 + 530.5 = 1,150.5 square inches
Therefore, the closest option is 1,171.5 in.2