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

Area of a Hexagon formula

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

\(\large{ A= 6 \;\left( \frac {1}{2} \;a\;h\; \right) }\)

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

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

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

Where:

\(\large{ A }\) = area

\(\large{ a }\) = edge

\(\large{ h }\) = height

\(\large{ Ac }\) = apothem circumcircle (outside radius)

\(\large{ Ai }\) = apothem incircle (inside radius)

\(\large{ N }\) = number of edges

\(\large{ \sin }\) = sine

\(\large{ \tan }\) = tangent

Edge of a Hexagon formula

\(\large{ a = \frac { p }   {6}   }\)

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

Where:

\(\large{ a }\) = edge

\(\large{ p }\) = perimeter

\(\large{ A }\) = area

Perimeter of a Hexagon formula

\(\large{ p= 6\;a }\)

Where:

\(\large{ p }\) = perimeter

\(\large{ a }\) = edge