Pentagonal Prism
20 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