| Name | Date |
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Fill in the characteristic listed at the top of each column for each regular polygon listed below, then find the polygon that has the greatest ratio of its area to the square of its perimeter. Assume that each side of each polygon has a measurement of one unit.
1. Which regular polygon contains the largest area compared to its perimeter?
2. What inferences or extrapolations can you make from your answer to question 1?
3. Do you think that an irregular polygon could contain a larger area for its perimeter? Why or why not?
| Number of Sides |
Name | Measurement in Degrees | Apothem | Perimeter | Area | Ratio of Area to the Square of the Perimeter | ||
|---|---|---|---|---|---|---|---|---|
| Exterior Angle | Interior Angle | Central Angle | ||||||
| 3 | ||||||||
| 4 | ||||||||
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| 12 | ||||||||