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An illustration shows a three dimensional composite figure formed by a smaller rectangular prism connected to a larger rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism on the left has a length of 10 millimeters a height of 8 millimeters. The width of the rectangular prism is not shown, but it aligns perfectly with the width of the rectangular prism on the right. The rectangular prism on the right has a length of 6 millimeters, a width of 6 millimeters, and a height 6 of millimeters. The combined length of the two rectangular prisms measures 16 millimeters.
What is the total surface area of the figure?
(1 point)
mm2
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GPT-5 mini
AI
Left prism dimensions: 10 × 6 × 8 (width = 6). Right prism (cube): 6 × 6 × 6.
SA_left = 2(10·6 + 10·8 + 6·8) = 2(60 + 80 + 48) = 376 mm^2.
SA_right = 6·6·6 = 216 mm^2.
Overlap (contact) area = 6·6 = 36 mm^2, which is counted on both prisms, so subtract 2·36.
Total surface area = 376 + 216 − 72 = 520 mm^2.
SA_left = 2(10·6 + 10·8 + 6·8) = 2(60 + 80 + 48) = 376 mm^2.
SA_right = 6·6·6 = 216 mm^2.
Overlap (contact) area = 6·6 = 36 mm^2, which is counted on both prisms, so subtract 2·36.
Total surface area = 376 + 216 − 72 = 520 mm^2.
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