Right Hexagonal Prism

Written by Jerry Ratzlaff on . Posted in Solid Geometry

• Right hexagon prism (a three-dimensional figure) is where each face is a regular polygon with equal sides and equal angles.
• Long diagonal always crosses the center point of the hexagon.
• Short diagonal does not cross the center point of the hexagon.
• 36 base diagonals
• 12 face diagonals
• 36 space diagonals
• 2 bases
• 18 edges
• 6 side faces
• 12 vertexs

Formulas that use Base Area of a Regular Hexagonal Prism

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

Where:

$$\large{A_b }$$ = base area

$$\large{ a }$$ = edge

Formulas that use Base Long Diagonal of a Regular Hexagon

 $$\large{ D_l = 2\;a }$$

Where:

$$\large{ D_l }$$ = long diagonal

$$\large{ a }$$ = edge

Formulas that use Base Short Diagonal of a Regular Hexagon

 $$\large{ D_s = \sqrt{3}\;a }$$

Where:

$$\large{ D_s }$$ = short diagonal

$$\large{ a }$$ = edge

Formulas that use Side Diagonal of a Regular Hexagonal Prism

 $$\large{ d' = \sqrt { a^2 + h^2 } }$$

Where:

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

$$\large{ a }$$ = edge

$$\large{ h }$$ = height

Formulas that use Edge of a Regular Hexagonal Prism

 $$\large{ a = \frac { A_{l} } { 6\;h } }$$ $$\large{ a = 3^{1/4}\; \sqrt {2\; \frac { V } { 9\;h } } }$$ $$\large{ a = \frac{1}{3} \; \sqrt { 3\;h^2 + \sqrt {3}\; A_s } - \sqrt {3}\; \frac {h}{3} }$$ $$\large{ a = 3^{1/4}\; \sqrt {2\; \frac { A_b } { 9 } } }$$

Where:

$$\large{ a }$$ = edge

$$\large{ h }$$ = height

$$\large{ A_b }$$ = base area

$$\large{ A_l }$$ = lateral surface area

$$\large{ A_s }$$ = surface area

$$\large{ V }$$ = volume

Formulas that use Height of a Regular Hexagonal Prism

 $$\large{ h = 2\; \sqrt {3}\; \frac { V } { 9\;a^2 } }$$ $$\large{ h = \frac {A_s} {6\;a } - \sqrt {3}\; \frac { a } {2 } }$$

Where:

$$\large{ h }$$ = height

$$\large{ a }$$ = edge

$$\large{ A_s }$$ = surface area

$$\large{ V }$$ = volume

Formulas that use Lateral Surface Area of a Regular Hexagonal Prism

 $$\large{ A_l = 6\;a\;h }$$

Where:

$$\large{ A_l }$$ = lateral surface area

$$\large{ a }$$ = edge

$$\large{ h }$$ = height

Formulas that use Surface Area of a Regular Hexagonal Prism

 $$\large{ A_s = 6\;a\;h + 3\; \sqrt 3\; a^2 }$$

Where:

$$\large{ A_s }$$ = surface area

$$\large{ a }$$ = edge

$$\large{ h }$$ = height

Formulas that use Volume of a Regular Hexagonal Prism

 $$\large{ V = \frac {3\; \sqrt {3} } { 2 } \; a^2\;h }$$

Where:

$$\large{ V }$$ = volume

$$\large{ a }$$ = edge

$$\large{ h }$$ = height

Tags: Equations for Volume