Hexagon

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • hexagon 2hexagon All edges are the same length.
  • Interior angles are 120°.
  • Exterior angles are 60°.
  • 9 diagonals
  • 6 edges
  • 6 vertexs

Edge formula

\(a = \frac { p }   {6}   \)

\(a = 3^{1/4} \sqrt { 2 \frac {A}{9} }  \)

Where:

\(a\) = edge

\(p\) = perimeter

\(A\) = area

Perimeter formula

\(p= 6a \)

Where:

\(p\) = perimeter

\(a\) = edge

Area formula

\(A =   \frac {3 \sqrt {3} } {2} a^2 \)

\(A= 6 \left( \frac {1}{2} ah \right) \)

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

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

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

Where:

\(A\) = area

\(a\) = edge

\(h\) = height

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

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

\(N\) = number of edges

\(\sin\) = sine

\(\tan\) = tangent