What is a prism: definition, elements, types, section options

In this publication, we will consider the definition, main elements, types and possible options for the section of a prism. The presented information is accompanied by visual drawings for better perception.

Definition of a prism

Prism is a geometric figure in space; a polyhedron with two parallel and equal faces (polygons), while the other faces are parallelograms.

The figure below shows one of the most common types of prism – quadrangular line (or parallelepiped). Other varieties of the figure are discussed in the last section of this publication.

Prism elements

For the picture above:

• Grounds are equal polygons. These can be triangles, four-, five-, hexagons, etc. In our case, these are parallelograms (or rectangles) ABCD и A₁B₁C₁D₁.
• Side faces are parallelograms: AA₁B₁B, BB₁C₁C, CC₁D₁D и AA₁D₁D.
• Side rib is a segment connecting the vertices of different bases corresponding to each other (AA₁, BB₁, CC₁ и DD₁). It is the common side of two side faces.
• Height (h) – this is a perpendicular drawn from one base to another, i.e. the distance between them. If the side edges are located at right angles to the bases of the figure, then they are also the heights of the prism.
• Base diagonal – a segment that connects two opposite vertices of the same base (AC, BD, A₁C₁ и B₁D₁). A triangular prism does not have this element.
• Side Diagonal A line segment that connects two opposite vertices of the same face. The figure shows the diagonals of only one face. (CD₁ и C₁D)so as not to overload it.
• Prism Diagonal – a segment connecting two vertices of different bases that do not belong to the same side face. We have shown only two of the four: AC₁ и B₁D.
• Prism surface is the total surface of its two bases and side faces. Formulas for calculation (for the correct figure) and prisms are presented in separate publications.

Prism sweep – the expansion of all the faces of the figure in one plane (most often, one of the bases). As an example, for a rectangular straight prism:

Note: prism properties are presented in .

Prism section options

1. Diagonal section – the cutting plane passes through the diagonal of the base of the prism and two corresponding side edges.Note: A triangular prism does not have a diagonal section, because The base of the figure is a triangle that has no diagonals.
2. Perpendicular Section – the cutting plane intersects all side edges at a right angle.

Note: other options for the section are not so common, so we will not dwell on them separately.

Prism types

Consider a variety of figures with a triangular base.

1. Straight prism – side faces are located at right angles to the bases (i.e. perpendicular to them). The height of such a figure is equal to its side edge.
2. Oblique prism – the side faces of the figure are not perpendicular to its bases.
3. Correct prism The bases are regular polygons. May be straight or oblique.
4. truncated prism – the part of the figure remaining after crossing it by a plane that is not parallel to the bases. It can also be both straight and inclined.