Basic geometry question regarding hexagons.

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SUMMARY

The discussion centers on calculating the longest diameter of an irregular hexagon with three distinct sets of sides, where each side is equal to its opposite but differs from adjacent sides. The participant seeks a formula incorporating three variables to represent these side lengths. It is established that the longest diameter may relate to half the perimeter, particularly in the context of a degenerate hexagon. Additionally, the role of angles in determining the diameter is questioned, indicating a need for further clarification on geometric principles.

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  • Understanding of irregular hexagon properties
  • Familiarity with perimeter calculations
  • Knowledge of geometric formulas
  • Basic trigonometry for angle considerations
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  • Research geometric properties of irregular hexagons
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Gazarai
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I'm trying to figure out how to find the longest diameter of any irregular hexagon with 3 different sets of sides. Each side is the same in length as the side opposite it, and different in length to both sides beside it. Any help?
 
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Err, I should note that I know *how* to find it, and that what I can't seem to figure out is how to put it into a formula, with 3 variables representing the 3 sets of sides.
 
Is the largest possible diameter not half the perimeter, using a degenerate hexagon?

Or is there something you haven't told us, say, regarding the angles?
 

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