# Regular Hexagon

on . 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 $$\large{ in }$$ $$\large{ mm }$$ 