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#### checkittwice

##### Member

- Apr 3, 2012

- 37

polygons

******with an odd number of sides, and each side length is

equal to 1 unit.

For examples, the polygon with the fewest number of sides in this group

is the equilateral triangle, and then the next one is an equilateral pentagon.

Has anyone thought about this?

The area of the equilateral triangle is [tex]\dfrac{\sqrt{3}}{4}[/tex] square units.

Is the area of any of these certain polygons (beyond the equilateral triangle)

less than [tex]\dfrac{\sqrt{3}}{4}[/tex] square units?

**Please,**do not attempt any sort of a proof. The one I saw

(and did not fully digest), is about two and a half pages long.

And, to me, I couldn't see the motivations for using the

strategies in the proof.

**** These are not limited to regular polygons in general.**

**The equilateral triangle happens to also be regular.**