## Introduction

In geometry, a nonagon is a nine-sided polygon or 9-gon. Calculate its area and perimeter.

# Nonagon Formulas Calculator

## Introduction

In geometry, a nonagon is a nine-sided polygon or 9-gon. Calculate its area and perimeter.

# Description

In geometry, a nonagon is a nine-sided polygon or 9-gon. Calculate its area and perimeter.

$A$, Symbol for Area;
${P}_{}$, Symbol for Perimeter;
${a}_{}$, Symbol for Side;

## Quote from Wikipedia

In geometry, a nonagon (/ˈnɒnəɡɒn/) or enneagon (/ˈɛniəɡɒn/) is a nine-sided polygon or 9-gon. The name "nonagon" is a prefix hybrid formation, from Latin (nonus, "ninth" + gonon), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century. The name "enneagon" comes from Greek enneagonon (εννεα, "nine" + γωνον (from γωνία = "corner")), and is arguably more correct,[1] though less common than "nonagon". The regular enneagon has Dih9 symmetry, order 18. There are 2 subgroup dihedral symmetries: Dih3 and Dih1, and 3 cyclic group symmetries: Z9, Z3, and Z1. These 6 symmetries can be seen in 6 distinct symmetries on the enneagon. John Conway labels these by a letter and group order.[3] Full symmetry of the regular form is r18 and no symmetry is labeled a1. The dihedral symmetries are divided depending on whether they pass through vertices (d for diagonal) or edges (p for perpendiculars), and i when reflection lines path through both edges and vertices. Cyclic symmetries in the middle column are labeled as g for their central gyration orders. Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only the g9 subgroup has no degrees of freedom but can seen as directed edges.

## Area

$A=\frac{9}{4}{a}^{2}\mathrm{cot}\left(\frac{{180}^{o}}{9}\right)$

# Output

## Perimeter

$P=9a$

# Output

## References

Figure - 24.1 https://www.redbubble.com/people/keplercat/works/27929051-nonagon-shape-black?p=poster