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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

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
6 months ago

To find the surface area of the two-tiered steps, we need to calculate the surface area of both rectangular prisms and then add them together.

Surface area of the large rectangular prism:
Front and back faces: 17 inches (length) * 6.5 inches (height) * 2 = 221 inches squared
Top and Bottom faces: 17 inches (length) * 8.5 inches (width) * 2 = 289 inches squared
Side faces: 6.5 inches (height) * 8.5 inches (width) * 2 = 110.5 inches squared

Surface area of the small rectangular prism:
Front and back faces: 14 inches (length) * 6.5 inches (height) * 2 = 182 inches squared
Top face: 14 inches (length) * 8.5 inches (width) = 119 inches squared
Side faces: (6.5 inches + 13 inches) * 8.5 inches * 2 = 204.5 inches squared

Now, add up the surface areas of both rectangular prisms:
221 + 289 + 110.5 + 182 + 119 + 204.5 = 1126 inches squared

So, the surface area of the two-tiered steps is 1,126 in.².