What is parallelepiped?

Translated from the Greek parallelogram means a plane. The parallelepiped is the prism, at the base of which lies the parallelogram. There are five types of parallelogram: inclined, straight and rectangular parallelepiped. The cube and rhomboater also belong to the parallelpiped and are its variety.

Before moving to the main concepts, let some definitions:

• The diagonal of the parallelepiped is a segment that combines the peaks of the parallelepiped, opposite each other.
• If two faces have a common edge, then you can call them adjacent ribs. If there is no common rib, then the faces are referred to as opposite.
• Two vertices that are not lying on one face are referred to opposite.

1

What properties has parallelepiped?

1. Lying on the opposite sides of the face of parallelepiped parallel to each other and are equal to each other.
2. If they are diagonal from one vertex to another, the intersection point of these diagonals will split them in half.
3. The parallelepiped side under the same and the same angle to the base will be equal. In other words, the angles of the airborne parties will be equal to each other.

2

What types of parallelepiped are?

Now we understand which parallelepipeds are. As already mentioned above, there are several types of this figure: straight, rectangular, inclined parallelepiped, as well as cube and rhombohedron. What do they differ among themselves? It's all about forming them planes and the corners that they form.

We will understand in more detail with each of the listed types of parallelepiped.

• As already understandable from the title, the inclined parallelepiped has inclined faces, namely such faces that are in relation to the base at an angle of 90 degrees.
• But a direct parallelepiped angle between the base and the edge is just ninety-degrees. It is for this reason that this type of parallelepiped has such a name.
• If all the faces of the parallelepiped are the same squares, you can consider this figure a cube.
• The rectangular parallelepiped received such a name due to the forming planes. If they are all rectangles (and the base, including), then this is a rectangular parallelepiped. This type of parallelepiped is not as often. Translated from the Greek Rhombohedron means a face or foundation. This is called a three-dimensional figure, in which the edges are diamonds.

3

Basic formulas for parallelepiped

The volume of parallelepiped is equal to the product of the base area on its height, perpendicular to the base.

The side surface area will be equal to the production of the perimeter of the base to height.
Knowing the main definitions and formulas can be calculated the base area and volume. The base can be chosen at its discretion. However, as a rule, a rectangle is used as a base.