Prism. Parallelepiped

author: Петя
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Българска версия:

• Definition: Polyhedral - with two equal n-walls and with n equal surrounded parallelograms , is called prism.

            The prism is:

1.right, if its surrounded edges are perpendicular on the radix;

2.regular, if the prism is right and its radix is regular poluhedral;

3.tilted, if its surrounded edges are not perpendicular on the plane of the radix.

Diagonal  on a prism is called the segment which connects two prism's vertix which are not from the same wall.

Height on a prism is called each line (which endings are from the planes on radixes) is perpendicular on these planes.

Lenght on each height is equal on the distance between radixes' planes.

• Definition: If prism has radixes which are parallelograms, then this prism is called parallelepiped.

            One parallelepiped is called right-angled when all its walls are rectangles.

            Cube - right-angled parallelepiped with walls which are squares.

           Parallelepiped's characteristics:

• Opposite walls are parallel and equal parallelograms.

• Parallelepiped has two diagonal intersections and 4 diagonals.

• Parallelepiped's diagonals intersect themselves in one point which devisits these diagonals in two equal segments.

            Right-angled parallelepiped's characteristics

• DIagonal intersections are equal rectangles;

• Its diagonals are equal;

• If its dementions are  a, b, c, and its diagonal is d, then d² = a² +b² +c².

            Area and  volume on prism

• surrounded area S is equal on the sum of surrounded walls' areas. Full area S₁ is equal on the sum of surrounded walls' areas and plus radixes' areas.