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Circle Cover Conclusion (Posted on 2016-07-07) Difficulty: 3 of 5
A circle of unit radius is completely covered by four identical regular hexagons.

What is the smallest area of each hexagon?

No Solution Yet Submitted by K Sengupta    
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Solution Interpretation 1: Non-overlap | Comment 1 of 2
Assuming the hexagons may not overlap.  Have three share a vertex and the fourth share a vertex with two of them.

If the hexagons have side 1, the circle has radius √(7)/2.  The problem asks for the circle to have radius 1 so the solution is the reciprocal of this: 2/√(7) ≈ .7559 for the side of a hexagon.
The area for each is then 6√(3)/7 ≈1.4846

Edited on July 7, 2016, 2:10 pm
  Posted by Jer on 2016-07-07 13:23:56

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