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Parallelepiped


Every prism whose bases are parallelograms is called parallelepiped. So we can have:


a) oblique parallelepiped


b) straight parallelepiped

If the straight parallelepiped has rectangular bases, it is called the parallelepiped rectangle, orthoedron or parallelepiped rectangle.

Rectangle parallelepiped

Be the parallelepiped rectangle of dimensions The, B and ç of figure:

We have four measuring edges The, four measuring edges B and four measuring edges ç; the edges indicated by the same letter are parallel.

Base and Cobblestone Diagonals

Consider the following figure:

dB = base diagonal

dP = diagonal of the cobblestone

In the ABFE base, we have:


In triangle AFD, we have:


Side area

Being THEL the lateral area of ​​a rectangle parallelepiped, we have:

THEL= ac + bc + ac + bc
THEL= 2ac + 2bc
THEL = 2 (ac + bc)

Total area

By planning the parallelepiped, we find that the total area is the sum of the areas of each pair of opposite faces:


THET= 2 (ab + ac + bc)

Volume

By definition, volume unit is an edge cube 1. Thus, considering a parallelepiped of dimensions 4, 2, and 2, we can break it down to 4. 2 . 2 edge cubes 1:

So the volume of a rectangular rectangle of dimensions The, B and ç It is given by:

V = abc

Since the two-dimensional product always results in the area of ​​one face and as any face can be considered as base, we can say that the volume of the rectangle parallelepiped is the product of the base area. THEBby height measurement H:

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