Common Prisms: Cube and Rectangular Parallelepiped

There are two very common prisms; the cube and rectangular parallelepiped. In non-mathematical term, both are called box.
 

Cube
Cube (Face and Space Diagonals)Cube is one of the Platonic Solids and is called regular hexahedron. It is a polyhedron whose six faces are all squares.
 

Properties of a Cube

  1. All edges of a cube are equal in length.
  2. All faces of the cube are congruent squares.

Formulas for Cube

Volume, V
$V = A_b \, h = a^3$

 

Total Area, A
$A = 6a^2$

 

Face Diagonal, d
$d = a\sqrt{2}$

 

Space Diagonal, s
$s = a\sqrt{3}$

 

Rectangular Parallelepiped (Cuboid)
rectangular-parallelepiped.jpgAll faces of rectangular parallelepiped are rectangles and two opposite faces are equal rectangles.
 

Properties of Rectangular Parallelepiped

  1. Parallel edges of rectangular parallelepiped are equal in length.
  2. Any two opposite faces of rectangular parallelepiped are equal and parallel rectangles.

Formulas for Rectangular Parallelepiped

Volume, V
$V = A_b \, h = abc$

 

Total Area, A
$A = 2(ab + bc + ac)$

 

Face Diagonals, d1, d2, and d3
$d_1 = \sqrt{a^2 + b^2}$

$d_2 = \sqrt{b^2 + c^2}$

$d_3 = \sqrt{a^2 + c^2}$

 

Space Diagonal, s
$s = \sqrt{a^2 + b^2 + c^2}$

 

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