Square Prism

Written by Jerry Ratzlaff on . Posted in Solid Geometry

 

square prism 2

square prism

  • 2 faces are square
  • 4 faces are rectangle
  • 4 base diagonals
  • 8 face diagonals
  • 4 space diagonals
  • 2 bases
  • 12 edges
  • 4 side faces
  • 8 vertexs

Edge formula

\(a = \frac {1} {2}   \sqrt {2D^2 + 2h^2} \)

\(a = \frac {1} {2}   \sqrt {4h^2 + 2A_s} -h \)

\(a = \sqrt { \frac {V} {h} } \)

Where:

\(a\) = edge

\(D\) = space diagonal

\(h\) = height

\(A_s\) = surface area

\(V\) = volume

Height formula

\(h = \frac {A_s} {4a} - \frac {a} {2} \)

\(h = \sqrt {D^2 + 2a^2} \)

Where:

\(h\) = height

\(A_s\) = surface area

\(a\) = edge

\(D\) = space diagonal

Diagonal formula

\(D = \sqrt {2a^2 + h^2} \)

Where:

\(D\) = space diagonal

\(a\) = edge

\(h\) = height

Base Area formula

\(A_b = a^2 \)

Where:

\(A_b\) = area

\(a\) = edge

Surface Area formula

\(A_s= 2a^2 + 4ah \)

Where:

\(A_s\) = surface area

\(a\) = area

\(h\) = height

Volume formula

\(V=a^2h \)

Where:

\(V\) = volume

\(a\) = edge

\(h\) = height