# Regular Hexagon

Written by Jerry Ratzlaff 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

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

Where:

$$\large{ A_{area} }$$ = area

$$\large{ a }$$ = edge

### Circumcircle Radius of a Regular Hexagon formula

$$\large{ R = a }$$

Where:

$$\large{ R }$$ = circumcircle radius

$$\large{ a }$$ = edge

### Edge of a Regular Hexagon formula

$$\large{ a = \frac { p } {6} }$$

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

Where:

$$\large{ a }$$ = edge

$$\large{ p }$$ = perimeter

$$\large{ A_{area} }$$ = area

### Inscribed Circle Radius of a Regular Hexagon formula

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

Where:

$$\large{ r }$$ = inside radius

$$\large{ a }$$ = edge

### Perimeter of a Regular Hexagon formula

$$\large{ p = 6 \;a }$$

Where:

$$\large{ p }$$ = perimeter

$$\large{ a }$$ = edge

### Long Diagonal of a Regular Hexagon formula

$$\large{ D' = 2 \;a }$$

Where:

$$\large{ D' }$$ = long diagonal

$$\large{ a }$$ = edge

### Short Diagonal of a Regular Hexagon formula

$$\large{ d' = \sqrt{3}\;a }$$

Where:

$$\large{ d' }$$ = short diagonal

$$\large{ a }$$ = edge