# Right Hexagonal Prism

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

## Base Area of a Right Hexagonal Prism formula

$$\large{ A_b = 3\; \sqrt {3}\; \frac { a^2 } { 2 } }$$
Symbol English Metric
$$\large{A_b }$$ = base area $$\large{ in^2 }$$  $$\large{ mm^2 }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$

## Base Long Diagonal of a Right Hexagon formula

$$\large{ D_l = 2\;a }$$
Symbol English Metric
$$\large{ D_l }$$ = long diagonal $$\large{ in }$$  $$\large{ mm }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$

## Base Short Diagonal of a Right Hexagon formula

$$\large{ D_s = \sqrt{3}\;a }$$
Symbol English Metric
$$\large{ D_s }$$ = short diagonal $$\large{ in }$$  $$\large{ mm }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$

## Side Diagonal of a Right Hexagonal Prism formula

$$\large{ d' = \sqrt { a^2 + h^2 } }$$
Symbol English Metric
$$\large{ d' }$$ = diagonal $$\large{ in }$$  $$\large{ mm }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$

## Edge of a Right Hexagonal Prism formulas

$$\large{ a = \frac { A_{l} } { 6\;h } }$$

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

$$\large{ a = \frac{1}{3} \; \sqrt { 3\;h^2 + \sqrt {3}\; A_s } - \sqrt {3}\; \frac {h}{3} }$$

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

Symbol English Metric
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ A_b }$$ = base area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ A_l }$$ = lateral surface area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ A_s }$$ = surface area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ V }$$ = volume $$\large{ in^3 }$$ $$\large{ mm^3 }$$

## Height of a Right Hexagonal Prism formulas

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

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

Symbol English Metric
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ A_s }$$ = surface area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ V }$$ = volume $$\large{ in^3 }$$ $$\large{ mm^3 }$$

## Lateral Surface Area of a Right Hexagonal Prism formula

$$\large{ A_l = 6\;a\;h }$$
Symbol English Metric
$$\large{ A_l }$$ = lateral surface area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$

## Surface Area of a Right Hexagonal Prism formula

$$\large{ A_s = 6\;a\;h + 3\; \sqrt 3\; a^2 }$$
Symbol English Metric
$$\large{ A_s }$$ = surface area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$

## Volume of a Right Hexagonal Prism formulas

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

$$\large{ V = 3 \; a \; b \; h }$$

Symbol English Metric
$$\large{ V }$$ = volume $$\large{ in^3 }$$ $$\large{ mm^3 }$$
$$\large{ b }$$ = center $$\large{ in }$$ $$\large{ mm }$$
$$\large{ a }$$ = edge $$\large{ in }$$ $$\large{ mm }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$

Tags: Volume Equations