Hexagon like many parallel lines

Formula collection

What is a regular hexagon?

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The regular hexagon consists of 6 equilateral triangles and in this case all interior angles are the same (namely $ 120 $ degrees). The diagonals that connect opposite corner points are all of the same length, are angular symmetries and axes of symmetry. The intersection of the diagonals is also the center of the incircle and the circumference.


What are the formulas for a regular hexagon?

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Standard formulas:
Area $ A $ of the regular hexagon: $ A = \ dfrac {3 \ times \ sqrt {3}} {2} \ times a ^ 2 \ approx 2.6 \ times a ^ 2 \ [4pt] $
Perimeter $ U $ of the regular hexagon: $ U = 6 \ cdot a \ [4pt] $

Extended formulas:
Incircle radius $ r_I $ of the regular hexagon: $ r_I = \ dfrac {a \ cdot \ sqrt {3}} {2} \ approx 0.87 \ cdot a \ [4pt] $
Perimeter radius $ r_U $ of the regular hexagon: $ r_U = a $
Long diagonal $ d $ of the regular hexagon: $ d = 2 \ cdot a $
Short diagonal $ d_ {2} $ of the regular hexagon: $ d_ {2} = \ sqrt {3} \ cdot a \ approx 1.73 \ cdot a $

(approximate formulas have been rounded to 2 decimal places)


Explanations of the variables used below.

Picture:



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Additional Information: [Edit] [version history]

Edges / corner points:

Edges: 6
Key points: 6

Information about the variables:

  • $ a $ is the Side length from the regular hexagon
  • $ A $ is that Area from the regular hexagon
  • $ U $ is that scopefrom the regular hexagon
  • $ r_I $ is the Inscribed circlefrom the regular hexagon
  • $ r_U $ is the Radiusfrom the regular hexagon
  • $ d $ is the long diagonalfrom the regular hexagon
  • $ e $ is the short diagonalfrom the regular hexagon


Interesting:

Regular hexagons also occur in nature: e.g. in crystal structures or honeycombs. These are also used in numerous board games, especially conflict simulation games such as "The Settlers of Catan".

Perimeter / incircle

Radius: Yes
Inscribed circle: yes