# Regular Hexagon

- Regular hexagon (a two-dimensional figure) is a polygon with six congruent sides.
- Circumcircle is a circle that passes through all the vertices of a two-dimensional figure.
- Congruent is all sides having the same lengths and angles measure the same.
- Diagonal is a line from one vertices to another that is non adjacent.
- Inscribed circle is the largest circle possible that can fit on the inside of a two-dimensional figure.
- Long diagonal always crosses the center point of the hexagon.
- Polygon (a two-dimensional figure) is a closed plane figure for which all edges are line segments and not necessarly congruent.
- Short diagonal does not cross the center point of the hexagon.
- Exterior angles are 60°.
- Interior angles are 120°.
- 9 diagonals
- 6 edges
- 6 vertexs

### Formulas that use Area of a Regular Hexagon

\(\large{ A_{area} = \frac {3}{2} \; \sqrt{3} \; a^2 }\) |

### Where:

\(\large{ A_{area} }\) = area

\(\large{ a }\) = edge

### Formulas that use Circumcircle Radius of a Regular Hexagon

\(\large{ R = a }\) |

### Where:

\(\large{ R }\) = circumcircle radius

\(\large{ a }\) = edge

### Formulas that use Edge of a Regular Hexagon

\(\large{ a = \frac { p } {6} }\) | |

\(\large{ a = 3^{1/4}\; \sqrt { 2\; \frac {A_{area}}{9} } }\) |

### Where:

\(\large{ a }\) = edge

\(\large{ p }\) = perimeter

\(\large{ A_{area} }\) = area

### Formulas that use Inscribed Circle Radius of a Regular Hexagon

\(\large{ r = \frac{ \sqrt{3} }{2} \; a }\) |

### Where:

\(\large{ r }\) = inside radius

\(\large{ a }\) = edge

### Formulas that use Perimeter of a Regular Hexagon

\(\large{ p = 6 \;a }\) |

### Where:

\(\large{ p }\) = perimeter

\(\large{ a }\) = edge

### Formulas that use Long Diagonal of a Regular Hexagon

\(\large{ D' = 2 \;a }\) |

### Where:

\(\large{ D' }\) = long diagonal

\(\large{ a }\) = edge

### Formulas that use Short Diagonal of a Regular Hexagon

\(\large{ d' = \sqrt{3}\;a }\) |

### Where:

\(\large{ d' }\) = short diagonal

\(\large{ a }\) = edge