# Hexagon like many parallel lines

## Formula collection

### What is a regular hexagon?

[Edit] [version history]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?

[Edit] [version history]**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:

**Additional Information:**[Edit] [version history]

### Edges / corner points:

Edges: 6Key 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
**scope**from the regular hexagon - $ r_I $ is the
**Inscribed circle**from the regular hexagon - $ r_U $ is the
**Radius**from the regular hexagon - $ d $ is the
**long diagonal**from the regular hexagon - $ e $ is the
**short diagonal**from 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: YesInscribed circle: yes

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