Right Hexagonal Prism

Written by Jerry Ratzlaff on . Posted in Solid Geometry

  • hexagonal prism 2Right 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

 

 

hexagonal prism 3

Base Area of a Regular Hexagonal Prism formula

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

Where:

\(\large{A_b }\) = base area

\(\large{ a }\) = edge

 

 

 

 

hexagonal prism 5Base Long Diagonal of a Regular Hexagon formula

\(\large{ D_l = 2\;a }\)

Where:

\(\large{ D_l }\) = long diagonal

\(\large{ a }\) = edge

Base Short Diagonal of a Regular Hexagon formula

\(\large{ D_s = \sqrt{3}\;a }\)

Where:

\(\large{ D_s }\) = short diagonal

\(\large{ a }\) = edge

hexagonal prism 6Side Diagonal of a Regular Hexagonal Prism formula

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

Where:

\(\large{ d' }\) = diagonal

\(\large{ a }\) = edge

\(\large{ h }\) = height

 

 

 

Edge of a Regular Hexagonal Prism formula

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

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

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

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

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

Height of a Regular Hexagonal Prism formula

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

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

Where:

\(\large{ h }\) = height

\(\large{ a }\) = edge

\(\large{ A_s }\) = surface area

\(\large{ V }\) = volume

Lateral Surface Area of a Regular Hexagonal Prism formula

\(\large{ A_l = 6\;a\;h }\)

Where:

\(\large{ A_l }\) = lateral surface area

\(\large{ a }\) = edge

\(\large{ h }\) = height

Surface Area of a Regular Hexagonal Prism formula

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

Where:

\(\large{ A_s }\) = surface area

\(\large{ a }\) = edge

\(\large{ h }\) = height

Volume of a Regular Hexagonal Prism formula

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

Where:

\(\large{ V }\) = volume

\(\large{ a }\) = edge

\(\large{ h }\) = height

 

Tags: Equations for Volume