Regular Hexagon

on 29 January 2016. Posted in Plane Geometry

Regular 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

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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Area of a Regular Hexagon formula