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How to find the volume of a parallelepiped

In a box of geometry - a three-dimensional number

In a box of geometry - a three-dimensional number generated by six parallelograms (rhomboid, the term is also sometimes used with the same meaning).



In Euclidean geometry, its definition coversAll four concepts (ie, a box, a parallelogram, a cube, and square). In this context, the geometry in which angles are not differentiated, it only allows the definition of a parallelogram parallelepiped. Three equivalent definitions of parallelepiped:
* Polyhedron with six sides (hexagon), each of which is a parallelogram,

* Hexagon with three pairs of parallel faces,

* Prism, based on - a parallelogram.


The rectangular cuboid (six rectangular faces), the cube (six square sides), and the six-party diamond are specific types box.


The volume of the box? set values ​​of its bases - A, and its height - H. Base - one of the six faces of the parallelepiped. Height - the perpendicular distance between the base and the opposite side.


An alternative method of determining the amount ofparallelepiped by using its vectors = (A1, A2, A3), b = (B1, B2, B3). The volume of the parallelepiped thus equal to the absolute value of the three values ​​- a? (? B c):
A = | b | | C | the degree of error in this case? = | B? c |,

where? - The angle between b and c, and the height

h = | a |, because?

where? - Internal angle between a and h.

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