To find the area of the polygon you've described, we need to visualize the shape based on the parameters given.
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Arrow Shape Roof: This likely indicates a quadrilateral base with a triangular roof on top. The "roof height" is given as 3 units.
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Base Dimensions: The dimensions "1,4,2,1,4,2" suggest lengths of different segments in the base, possibly creating a pattern or effectively describing the width at certain points.
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Inside "3,3": This part likely describes an inner rectangle or an additional feature inside the main shape, but it needs clarity with the diagram to be precise.
Steps to find the area:
If we interpret "1, 4, 2, 1, 4, 2" to mean a shape whose base starts at width 1 unit, expands to 4 units, has a segment of 2 units, then returns back to 1 unit and expands again to 4 units, we will break it into identifiable segments.
Given that we have a "roof height" of 3:
- The top triangular part's area can be calculated by taking the base width where the roof spans.
- If the triangular part has a base that effectively spans 7 units (1 + 4 + 2), the triangle's area would be 1/2 * base * height → \( \frac{1}{2} \times 7 \times 3 \).
Calculation:
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Calculating Triangle Area: \[ \text{Area}_{triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 \times 3 = 10.5 \text{ square units} \]
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Calculating the Base Area: Assume the bottom part where the boundary is formed creates a rectangular or polygonal shape. We will need to create the shape to understand the area size descriptively and with axes referenced to account for overlaps.
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Total Area: The total area is thus a summation of the triangular roof's area and the area beneath the arrow, as well as any other rectangular features specified.
If you can provide more specific details or a visual representation (though it may not be visible here), I could finalize calculations. As it is, based on the provided options:
- 36 square units
- 54 square units
- 42 square units
- 72 square units
Without clear dimensions to evaluate every fugue accurately, typically, from these options, if you calculate the area from basic assumptions, 36 square units might closely align as a potential output from the assumptions laid out.
In conclusion, based on roofing structures, and congruency assumptions hinted, I urge reevaluation against a provided visual and rigorously laying out mentioned segments' exact total areas.