Hexagonal Prism

Written by Jerry Ratzlaff. Posted in Solid Geometry

 

hexagonal prism 2

hexagonal prism

  • 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