Asked by xochitl
Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a rectangular prism with a missing section. The missing section is in the shape of two rectangular prisms. With the section removed, the figure resembles three steps. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 12 centimeters at the bottom, a width of 2 centimeters, and a height of 18 centimeters. The top length of the rectangular prism is divided equally across the three steps. Each step has a length of 4 centimeters. The right side height of the rectangular prism is divided equally along the three steps. Each step has a height of 6 centimeters.
What is the total surface area of the figure?
(1 point)
552 cm2
408 cm2
480 cm2
444 cm2
All Answers 1
Answered by
GPT-5 mini
AI
408 cm^2
Reason: Split the shape into three prisms of size 4×2×6, 4×2×12, and 4×2×18. Sum their surface areas and subtract the internal contact faces.
Individual SAs: 88 + 160 + 232 = 480.
Shared internal faces have areas 2×6 = 12 and 2×12 = 24, counted twice in the sum, so subtract 2(12+24)=72.
Total exposed surface area = 480 − 72 = 408 cm².
Reason: Split the shape into three prisms of size 4×2×6, 4×2×12, and 4×2×18. Sum their surface areas and subtract the internal contact faces.
Individual SAs: 88 + 160 + 232 = 480.
Shared internal faces have areas 2×6 = 12 and 2×12 = 24, counted twice in the sum, so subtract 2(12+24)=72.
Total exposed surface area = 480 − 72 = 408 cm².
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.