# 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 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

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

Formulas for Cube

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

$A = 6a^2$

$d = a\sqrt{2}$

$s = a\sqrt{3}$

**Rectangular Parallelepiped (Cuboid)**

All faces of rectangular parallelepiped are rectangles and two opposite faces are equal rectangles.

Properties of Rectangular Parallelepiped

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

Formulas for Rectangular Parallelepiped

$V = A_b \, h = abc$

$A = 2(ab + bc + ac)$

_{1}, d

_{2}, and d

_{3}

$d_1 = \sqrt{a^2 + b^2}$

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

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

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