Surface Area of Composite 3D Figures Practice
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Question
Use the image to answer the question.
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)
To find the total surface area of the figure, we need to find the surface area of each rectangular prism and then add them together.
Surface area of the rectangular prism on the left:
- Front and back faces: 10mm * 8mm * 2 = 160mm²
- Top and bottom faces: 10mm * w * 2 (since the width is not given) = 20w mm²
- Right and left faces: 8mm * w * 2 = 16w mm²
Surface area of the rectangular prism on the right:
- Front and back faces: 6mm * 6mm * 2 = 72mm²
- Top and bottom faces: 6mm * 6mm * 2 = 72mm²
- Right and left faces: 6mm * 6mm * 2 = 72mm²
Total surface area = 160mm² + 20w mm² + 16w mm² + 72mm² + 72mm² + 72mm²
Total surface area = 396mm² + 36w mm²
Since the combined length of the two rectangular prisms is 16mm, we can find the width of the left rectangular prism:
10mm + 6mm + 6mm = 16mm
16mm - 10mm - 6mm = w
w = 0mm
Substitute w = 0mm back into the total surface area equation:
Total surface area = 396mm² + 36(0) mm²
Total surface area = 396mm²
The total surface area of the figure is 396mm².