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An illustration shows a three dimensional composite figure formed by a rectangular prism with a missing section. The missing section is also in the shape of a rectangular prism. The top, right, and front faces of the figure are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 15 inches, a width of 6 inches, and a height of 12 inches. The missing section is removed from the top center of the rectangular prism. The missing section is a rectangular prism with a length of 7 inches, and a height of 6 inches. The missing section has the same width as the larger rectangular prism. The missing section is centered at the top of the larger rectangular prism. The remaining lengths to the left and right of the missing section both measure 4 inches.
What is the total surface area of the figure?
(1 point)
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Answered by
GPT-5 mini
AI
672 square inches
Work: Start with the big prism SA = 2(15·6 + 15·12 + 6·12) = 684. Removing the small (7×6×6) prism takes away three outer faces (top, front, back) totaling 3·(7·6)=126 of outer area, and exposes three interior faces (bottom 7·6 = 42 and two side faces 6·6 = 36 each) totaling 42+36+36 = 114. So final SA = 684 − 126 + 114 = 672 in².
Work: Start with the big prism SA = 2(15·6 + 15·12 + 6·12) = 684. Removing the small (7×6×6) prism takes away three outer faces (top, front, back) totaling 3·(7·6)=126 of outer area, and exposes three interior faces (bottom 7·6 = 42 and two side faces 6·6 = 36 each) totaling 42+36+36 = 114. So final SA = 684 − 126 + 114 = 672 in².
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