To determine the total surface area of the upside-down "L" shape based on the measurements provided, we must first break down the shape into recognizable sections. The given dimensions suggest that the shape is made of rectangular components.
Step-by-step breakdown
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Identify all sections of the "L" shape:
- Bottom horizontal section.
- Left vertical section.
- Right vertical section.
- Top horizontal section.
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Dimensions:
- Bottom width: 6.2 cm
- Left height: 11.5 cm
- Right height: 7.5 cm
- The height above the "corner" (the part of the "L" where it turns) is 4 cm (the height above the angle)
- The top horizontal section length is 13.7 cm.
Calculation of Areas:
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Bottom horizontal section (rectangle):
- Width = 6.2 cm
- Height = 4 cm (from angle to the top)
- Area = \(6.2 \times 4 = 24.8 , \text{cm}^2\)
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Left vertical rectangle:
- Width = 4 cm
- Height = 11.5 cm
- Area = \(4 \times 11.5 = 46 , \text{cm}^2\)
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Right vertical rectangle:
- Width = 7.5 cm
- Height = 7.5 cm (given it is above the angle)
- Area = \(7.5 \times 7.5 = 56.25 , \text{cm}^2\)
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Top horizontal section (rectangle):
- Length = 13.7 cm
- Height = 4 cm
- Area = \(13.7 \times 4 = 54.8 , \text{cm}^2\)
Total Area Calculation:
Now, let’s add all the areas together:
\[ \text{Total Area} = 24.8 + 46 + 56.25 + 54.8 = 181.85 , \text{cm}^2 \]
However, this result appears to be inconsistent with the answer choices provided in your question.
Thus, you may need to clarify the specific orientation or other dimensions pertaining to the surface area calculations, or confirm the dimensions to ensure the proper calculation for the given figure.
If the figure provided includes additional elements such as thickness or if it is a solid object (not just the surface) but a hollow “L” structure or otherwise, the calculation would be different. Please revisit the figure and its levels to ensure all details align, or provide additional clarification regarding its 3D nature, if applicable.
Based on the provided responses, I cannot confirm which of the options would be correct without additional information or potential corrections on measurements.