Question

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)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of the two-tiered steps, we first need to find the surface area of each individual rectangular prism and then add them together.

For the large rectangular prism on the bottom:
- Front and back faces: 17 inches (length) * 6.5 inches (height) = 110.5 square inches each
- Top and bottom faces: 17 inches (length) * 8.5 inches (width) = 144.5 square inches each
- Left and right faces: 6.5 inches (height) * 8.5 inches (width) = 55.25 square inches each
Surface area of large rectangular prism: 2(110.5) + 2(144.5) + 2(55.25) = 221 + 289 + 110.5 = 620 square inches

For the small rectangular prism on top:
- Front and back faces: 14 inches (length) * 6.5 inches (height) = 91 square inches each
- Top and bottom faces: 14 inches (length) * 8.5 inches (width) = 119 square inches each
- Left and right faces: 6.5 inches (height) * 8.5 inches (width) = 55.25 square inches each
Surface area of small rectangular prism: 2(91) + 2(119) + 2(55.25) = 182 + 238 + 110.5 = 530.5 square inches

Total surface area of the two-tiered steps: 620 (large rectangular prism) + 530.5 (small rectangular prism) = 1150.5 square inches

Therefore, the surface area of the two-tiered steps is 1150.5 square inches.