Volume of Parallelepiped
A parallelepiped is a very tongue twisted
name for a three dimensional square, rectangle or
parallelogram. Any cardboard box you see around is most likely
a parallelepiped. If the box is upright, in another word, the
sides are perpendicular to the base of the box, then the
mathematical term for that box is rectangular parallelepiped.
So, before we calculate the volume of a parallelepiped, let us
examine closely the differences between a rectangular
parallelepiped and other parallelepiped, as well as what a
parallelepiped actually is.
This parcel cardboard box is an example of a
parallelepiped. Because the box is upright and the sides are
perpendicular to the base, it is also an example of a
rectangular parallelepiped. Let's examine its geographical
shape in more detail.
Rectangular parallelepiped
The rectangular parallelepiped is a 3  D
version of a rectangle or a square where b is
perpendicular to a. A rectangular
parallelepiped is made up of 6 rectangles. Now we compare this
rectangular parallelepiped to other types of
parallelepipeds.
Only rectangular parallelepiped has
perpendicular sides. Other parallelepiped can have slanted
sides. In another word, a parallelepiped is made up of six
parallelograms where a, b, and c are unique dimensions. A in
the diagram represents the area of a side of the parallelepiped
which we are going to use to calculate the volume. If you do
not know the area A, then you can use the formula for the area
of a parallelogram to calculate A first. Just to recap, the
area of a parallelogram is just its base times perpendicular
height.
Another measurement we need to make before
we can calculate the volume of the parallelepiped is the height
between A and its parallel side. The height is given by
h in the diagram. Note that h has to be
perpendicular to the side which you just calculated the area
of. It cannot be any slanted side of the parallelepiped.
Now we are ready to calculate the volume of
a parallelepiped using this formula.
