Use the image to answer the question.

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

1,409.5 in.2
1,409.5 in. squared

1,171.5 in.2
1,171.5 in. squared

2,320.5 in.2
2,320.5 in. squared
Skip to navigation

page 17 of 17

Answer 1

First, calculate the surface area of the bottom rectangular prism:

Surface area = 2(length * width + length * height + width * height)
Surface area = 2(17 * 14 + 17 * 6.5 + 14 * 6.5)
Surface area = 2(238 + 110.5 + 91)
Surface area = 2(439.5)
Surface area = 879 square inches

Next, calculate the surface area of the top rectangular prism that is not covered by the small rectangular prism:

Surface area = length * width + length * height + width * height
Surface area = 8.5 * 14 + 8.5 * 6.5 + 14 * 6.5
Surface area = 119 + 55.25 + 91
Surface area = 265.25 square inches

Add the surface area of both prisms to get the total surface area of the two-tiered steps:

Total surface area = Surface area of bottom prism + Surface area of top prism
Total surface area = 879 + 265.25
Total surface area = 1,144.25

The surface area of the two-tiered steps is 1,144.25 square inches.

Therefore, the correct answer is:

1,144.25 in. squared