In geometry, the parallelepiped is a three-dimensional number formed by six parallelograms (the term rhomboid is also sometimes used with this value).
In the Euclidean geometry, its definition coversAll four concepts (that is, a parallelepiped, a parallelogram, a cube, and a square). In this context of geometry, in which angles are not differentiated, its definition admits only a parallelogram and a parallelepiped. Three equivalent definitions of the parallelepiped:
* Polyhedron with six faces (hexagon), each of which is a parallelogram,
* Hexahedron with three pairs of parallel faces,
* Prism, the basis of which is a parallelogram.
Rectangular cuboid (six rectangular faces), a cube (six square sides), and a six-sided rhombus are concrete types of parallelepiped.
The volume of a parallelepiped? The totality of the values of its base is A and its height is H. The base is one of the six faces of the parallelepiped. Height - perpendicular distance between the base and the opposite side.
An alternative method for determining the volumeThe parallelepiped is realized by means of its vectors = (A1, A2, A3), b = (B1, B2, B3). The volume of a parallelepiped, therefore, is equal to the absolute value of three values - a? (B? C):
A = | b | | C | Degree of error in this case? = | B? C |,
Where? - angle between b and c, and height
H = | a |, because?,
Where? - The internal angle between a and h.