Octagon

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • All edges are the same lengthoctagon 2octagon
  • Interior angles are 135°
  • Exterior angles are 45°
  • 20 diagonals
  • 8 edges
  • 8 vertexs

Edge formula

\(a = \sqrt { {\sqrt 2} \frac {A}{2} - \frac {A}{2} }   \)

\(a = \frac {p}{8}   \)

Where:

\(a\) = edge

\(A\) = area

\(p\) = perimeter

Perimeter formula

\(p= 8a \)

Where:

\(p\) = perimeter

\(a\) = edge

Area formula

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

\(A = 8 \left( \frac {1} {2} ah \right) \)

\(A = \frac { a^2 N }   { 4 \tan \left( \frac {180°} {N} \right) } \)

\(A = \frac { Ac^2 N \sin \left( \frac {360°} {N} \right) }   {2}   \)

\(A = Ai^2 N \tan \left( \frac {180°} {N} \right)   \)

Where:

\(A\) = area

\(a\) = edge

\(Ac\) = apothem circumcircle (outside radius)

\(Ai\) = apothem incircle (inside radius)

\(N\) = number of edges

\(\sin\) = sine

\(\tan\) = tangent