# Hexagonal Prism

Written by Jerry Ratzlaff on . Posted in Solid Geometry

• 36 base diagonals
• 12 face diagonals
• 36 space diagonals
• 2 bases
• 18 edges
• 6 side faces
• 12 vertexs

## Edge formula

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

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

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

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

Where:

$$a$$ = edge

$$h$$ = height

$$A_b$$ = base area

$$A_l$$ = lateral surface area

$$A_s$$ = surface area

$$V$$ = volume

## Height formula

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

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

Where:

$$h$$ = height

$$a$$ = edge

$$A_s$$ = surface area

$$V$$ = volume

## Base Area formula

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

Where:

$$A_b$$ = base area

$$a$$ = edge

## Lateral Surface Area formula

$$A_l = 6ah$$

Where:

$$A_l$$ = lateral surface area

$$a$$ = edge

$$h$$ = height

## Surface Area formula

$$A_s = 6ah + 3 \sqrt 3 a^2$$

Where:

$$A_s$$ = surface area

$$a$$ = edge

$$h$$ = height

## Volume formula

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

Where:

$$V$$ = volume

$$a$$ = edge

$$h$$ = height

Tags: Equations for Volume