# Regular Heptagon

- Regular heptagon (a two-dimensional figure) is a polygon with seven 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.
- Polygon (a two-dimensional figure) is a closed plane figure for which all edges are line segments and not necessarly congruent.
- Exterior angles are 51.429°
- Interior angles are 128.571°
- 14 diagonals
- 7 edges
- 7 vertexs

## Formulas that use Area of a Regular Heptagon formula

\(\large{ A_{area} = \frac {7} {4} \;a^2 \; \cot \;\left( \frac {180°} {7} \right) }\) |

### Where:

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

\(\large{ a }\) = edge

\(\large{ \cot }\) = cotangent

## Formulas that use Edge of a Regular Heptagon

\(\large{ a = \frac {p}{7} }\) |

### Where:

\(\large{ a }\) = edge

\(\large{ p }\) = perimeter

## Formulas that use Perimeter of a Regular Heptagon

\(\large{ p= 7 \;a }\) |

### Where:

\(\large{ p }\) = perimeter

\(\large{ a }\) = edge