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Home / The science / Mathematics / How to find the volume of a parallelepiped

How to find the volume of a box


In geometry, a box is a three-dimensional number

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.

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