Regular Hexagon

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

Regular Hexagon Index

 

Area of a Regular Hexagon formula

\(\large{ A_{area} =   \frac {3}{2} \; \sqrt{3} \; a^2 }\) 
Symbol English Metric
\(\large{ A_{area} }\) = area  \(\large{ in^2 }\)  \(\large{ mm^2 }\) 
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)

 

Circumcircle Radius of a Regular Hexagon formula

\(\large{ R = a   }\) 
Symbol English Metric
\(\large{ R }\) = circumcircle radius \(\large{ in }\) \(\large{ mm }\)
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)

  

Edge of a Regular Hexagon formulas

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

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

Symbol English Metric
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)
\(\large{ A_{area} }\) = area  \(\large{ in^2 }\)  \(\large{ mm^2 }\) 
\(\large{ p }\) = perimeter \(\large{ in }\)  \(\large{ mm }\) 

 

Inscribed Circle Radius of a Regular Hexagon formula

\(\large{ r = \frac{ \sqrt{3} }{2} \; a  }\) 
Symbol English Metric
\(\large{ r }\) = inside radius \(\large{ in }\) \(\large{ mm }\)
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)

  

Perimeter of a Regular Hexagon formula

\(\large{ p =  6 \;a }\) 
Symbol English Metric
\(\large{ p }\) = perimeter \(\large{ in }\) \(\large{ mm }\)
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)

 

Long Diagonal of a Regular Hexagon formula

\(\large{ D' = 2 \;a }\) 
Symbol English Metric
\(\large{ D' }\) = long diagonal \(\large{ in }\) \(\large{ mm }\)
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)

  

Short Diagonal of a Regular Hexagon formula

\(\large{ d' = \sqrt{3}\;a }\) 
Symbol English Metric
\(\large{ d' }\) = short diagonal \(\large{ in }\) \(\large{ mm }\)
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)

 

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