﻿ Octagon Formulas Calculator

## Introduction

An octagon is a eight-sided polygon or 8-gon, which means that it has eight equal side. Calculate its perimeter and area.

# Octagon Formulas Calculator  ## Introduction

An octagon is a eight-sided polygon or 8-gon, which means that it has eight equal side. Calculate its perimeter and area.

# Description

An octagon is a eight-sided polygon or 8-gon, which means that it has eight equal side. Calculate its perimeter and area.

$a$, Symbol for Side;
$p$, Symbol for Perimeter;
$A$, Symbol for Area; ## Quote from Wikipedia

The sum of all the internal angles of any octagon is 1080°. As with all polygons, the external angles total 360°. If squares are constructed all internally or all externally on the sides of an octagon, then the midpoints of the segments connecting the centers of opposite squares form a quadrilateral that is both equidiagonal and orthodiagonal (that is, whose diagonals are equal in length and at right angles to each other).:Prop. 9 The midpoint octagon of a reference octagon has its eight vertices at the midpoints of the sides of the reference octagon. If squares are constructed all internally or all externally on the sides of the midpoint octagon, then the midpoints of the segments connecting the centers of opposite squares themselves form the vertices of a square.:Prop. 10

## Perimeter of an octagon

$8a$

# Output

## Area of an octagon

$2{a}^{2}\left(1+\sqrt{2}\right)$

# Output

## References

Figure - 16.1 By László Németh - Own work, CC0, https://commons.wikimedia.org/w/index.php?curid=27295120