To calculate the area of the "H" shaped polygon defined by the dimensions provided (12, 3, 6, 5, 3, 12, 5), we can visualize the "H" shape and break it down into simpler components.
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The total height of the "H" shape: This seems to be defined by the vertical segments. The height can be taken as the length of the vertical pieces, which is \( 12 \) (the total vertical extent).
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The width of the "H" shape can be determined by the dimensions provided. The widths 3, 6, and 5 indicate segments of the polygon:
- The two vertical bars of the "H" each have width \( 3 \) and \( 5 \) respectively.
Thus, we can model the "H" composed of:
- A rectangle for the left vertical section.
- A rectangle for the right vertical section.
- A rectangle for the horizontal cross section that connects the two vertical bars.
Step-by-Step Calculation
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Left Vertical Rectangle:
- Width = 3
- Height = 12
- Area = Width × Height = \( 3 \times 12 = 36 \)
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Right Vertical Rectangle:
- Width = 5
- Height = 12
- Area = Width × Height = \( 5 \times 12 = 60 \)
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Horizontal Cross Bar:
- Width = the middle section, which is \( 6 \) (the width measured from the left bar to the right bar).
- Height = 3 (the dimension given).
- Area = Width × Height = \( 6 \times 3 = 18 \)
Total Area Calculation:
Now add all the areas together: \[ \text{Total Area} = \text{Area of Left Vertical} + \text{Area of Right Vertical} + \text{Area of Horizontal Cross Bar} \] \[ \text{Total Area} = 36 + 60 + 18 = 114 \]
Therefore, the area of the H shaped polygon is \( \boxed{114} \).