Regular Hexagon

Written by Jerry Ratzlaff on . Posted in Plane Geometry

  • regular hexagon 6Regular hexagon (a two-dimensional figure) is a polygon with six congruent sides.
  • Circumcircle is a circle that passes through all the vertices of a two-dimensional figure.
  • Congruent is all sides having the same lengths and angles measure the same.
  • Diagonal is a line from one vertices to another that is non adjacent.
  • Inscribed circle is the largest circle possible that can fit on the inside of a two-dimensional figure.
  • Long diagonal always crosses the center point of the hexagon.
  • Polygon (a two-dimensional figure) is a closed plane figure for which all edges are line segments and not necessarly congruent.
  • Short diagonal does not cross the center point of the hexagon.
  • Exterior angles are 60°.
  • Interior angles are 120°.
  • 9 diagonals
  • 6 edges
  • 6 vertexs

 

Formulas that use Area of a Regular Hexagon

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

Where:

\(\large{ A_{area} }\) = area

\(\large{ a }\) = edge

 

Formulas that use Circumcircle Radius of a Regular Hexagon

\(\large{ R = a   }\)   

Where:

\(\large{ R }\) = circumcircle radius

\(\large{ a }\) = edge

 

Formulas that use Edge of a Regular Hexagon

\(\large{ a = \frac { p }   {6}   }\)   
\(\large{ a = 3^{1/4}\; \sqrt { 2\; \frac {A_{area}}{9} }  }\)   

Where:

\(\large{ a }\) = edge

\(\large{ p }\) = perimeter

\(\large{ A_{area} }\) = area

 

Formulas that use Inscribed Circle Radius of a Regular Hexagon

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

Where:

\(\large{ r }\) = inside radius

\(\large{ a }\) = edge

 

Formulas that use Perimeter of a Regular Hexagon

\(\large{ p =  6 \;a }\)   

Where:

\(\large{ p }\) = perimeter

\(\large{ a }\) = edge

 

Formulas that use Long Diagonal of a Regular Hexagon

\(\large{ D' = 2 \;a }\)   

Where:

\(\large{ D' }\) = long diagonal

\(\large{ a }\) = edge

 

Formulas that use Short Diagonal of a Regular Hexagon

\(\large{ d' = \sqrt{3}\;a }\)   

Where:

\(\large{ d' }\) = short diagonal

\(\large{ a }\) = edge