Right Square Prism

Written by Jerry Ratzlaff on . Posted in Solid Geometry

  • square prism 2right square prism 1Right square prism (a three-dimensional figure) has square bases, four faces that are rectangles with equal sides and equal angles.
  • Diagonal is a line from one vertices to another that is non adjacent.
  • 1 base
  • 12 edges
  • 5 faces
  • 8 vertexs
  • 2 base diagonals
  • 10 face diagonals
  • 4 space diagonals

Base Area of a Right Square Prism formula

\(\large{ A_b = a^2 }\)

Where:

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

\(\large{ a }\) = edge

Diagonal of a Right Square Prism formula

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

Where:

\(\large{ D' }\) = space diagonal

\(\large{ a }\) = edge

\(\large{ h }\) = height

Edge of a Right Square Prism formula

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

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

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

Where:

\(\large{ a }\) = edge

\(\large{ h }\) = height

\(\large{ D' }\) = space diagonal

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

\(\large{ V }\) = volume

Height of a Right Square Prism formula

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

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

Where:

\(\large{ h }\) = height

\(\large{ a }\) = edge

\(\large{ D' }\) = space diagonal

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

Surface Area of a Right Square Prism formula

\(\large{ A_s= 2\;a^2 + 4\;a\;h }\)

Where:

\(\large{ A_s }\) = surface area (bottom, top, sides)

\(\large{ a }\) = area

\(\large{ h }\) = height

Volume of a Right Square Prism formula

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

Where:

\(\large{ V }\) = volume

\(\large{ a }\) = edge

\(\large{ h }\) = height