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
2,320.5 in.2
2,320.5 in. squared
1,409.5 in.2
1,409.5 in. squared
1,171.5 in.2
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.
For the larger rectangular prism on the bottom:
Surface area = 2lw + 2lh + 2wh
Surface area = 2(17)(6.5) + 2(17)(8.5) + 2(6.5)(8.5)
Surface area = 221 + 289 + 110.5
Surface area = 620.5 in²
For the smaller rectangular prism on the top:
Surface area = 2lw + 2lh + 2wh
Surface area = 2(14)(6.5) + 2(14)(13) + 2(6.5)(13)
Surface area = 182 + 364 + 169
Surface area = 715 in²
Adding the surface areas of both rectangular prisms together:
Total surface area = 620.5 + 715
Total surface area = 1335.5 in²
Therefore, the surface area of the two-tiered steps is 1335.5 in².