To find the surface area of the two-tiered steps, we need to find the surface area of both rectangular prisms separately and then add them together.
Surface area of the large rectangular prism:
- Top and bottom: 17 inches * 14 inches = 238 square inches (x2 for both top and bottom)
- Front and back: 17 inches * 6.5 inches = 110.5 square inches (x2 for both front and back)
- Sides: 14 inches * 6.5 inches = 91 square inches (x2 for both sides)
Total surface area of the large rectangular prism = 476 + 221 + 182 = 879 square inches
Surface area of the small rectangular prism:
- Top and bottom: 8.5 inches * 14 inches = 119 square inches (x2 for both top and bottom)
- Front and back: 8.5 inches * 6.5 inches = 55.25 square inches (x2 for both front and back)
- Sides: 14 inches * 6.5 inches = 91 square inches (x2 for both sides)
Total surface area of the small rectangular prism = 238 + 110.5 + 182 = 530.5 square inches
Total surface area of the two-tiered steps = 879 + 530.5 = 1,409.5 square inches
Therefore, the surface area of the two-tiered steps is 1,409.5 in. squared.
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
1,409.5 in.2
1,409.5 in. squared
1,171.5 in.2
1,171.5 in. squared
879 in.2
879 in. squared
2,320.5 in.2
2,320.5 in. squared
Skip to navigation
1 answer