Pentagonal Prism

Written by Jerry Ratzlaff on . Posted in Solid Geometry

 

pentagonal prism 2

  • pentagonal prism20 base diagonals
  • 10 face diagonals
  • 20 space diagonals
  • 2 bases
  • 15 edges
  • 5 side faces
  • 10 vertexs

Edge formula

\(a = 25^{3/4}   {\frac   {\sqrt {A_b} }     { 5 \left( \sqrt {20} +5 \right) ^1/4 }   } \)

\(a = \frac   { - \left ( 5 \sqrt {5} h  - \sqrt { 125h^2 + 10 A_s \sqrt { \sqrt {500} +25 }   }   \right) }     { 5 \sqrt { \sqrt { 20 } +5 }  } \)

\(a = \frac {A_l}   {5h} \)

Where:

\(a\) = edge

\(A_b\) = base area

\(A_l\) = lateral surface area

\(A_s\) = surface area

\(h\) = height

Height formula

\(h = \frac {A_s} {5a} -   \frac {1}{10}a \sqrt { \sqrt {500} +25 } \)

Where:

\(h\) = height

\(A_s\) = surface area

\(a\) = edge

Base Area formula

\(A_b= \frac {1}{4} \sqrt { 5 \left( 5+2 \sqrt {5} \right) a^2 } \)

Where:

\(A_b\) = base area

\(a\) = edge

Lateral Surface Area formula

\(A_l = 5ah \)

Where:

\(A_l\) = lateral surface area

\(a\) = edge

\(h\) = height

Surface Area formula

\(A_s = 5ah + \frac {1}{2}   \sqrt { 5 \left ( 5+2 \sqrt {5} \right) } a^2   \)

Where:

\(A_s\) = surface area

\(a\) = edge

\(h\) = height

Volume formula

\(V= \frac {1}{4}   \sqrt { 5 \left ( 5+2 \sqrt {5} \right) } a^2h \)

Where:

\(V\) = volume

\(a\) = edge

\(h\) = height