Prism. Characteristics and types

A prism is a polyhedron, the vertices of which are located on two parallel planes, and all its edges lying outside these planes are parallel to each other. What are the formulas for calculating the volume and area of ​​a prism? What is this polyhedron characterized by?

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1. Types of prism

A prism is a polyhedron whose vertices are located on parallel planes, which are called the bases of the prism. Its edges, lying outside the bases, are parallel to each other.

We can divide the prisms into three types:

  • straight prisms - all walls are rectangles, the edges of the side walls are perpendicular to the bases;
  • inclined prisms - their walls are parallelograms, and the body is inclined;
  • Archimedean prism - normal prism with the base edge of the same length as the height.

A normal prism is a simple prism with a regular polygon in its base.

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1.1. Simple prism

The prism has two congruent polygonal bases that lie on parallel planes. The side walls are rectangles perpendicular to the bases. The name of this figure depends on the polygon underlying it.

Examples of simple prisms are cuboids and cubes. If the base of a simple prism is a regular polygon (e.g. a square, an equilateral triangle, a regular hexagon), then such a prism is called a regular polygon.

1.2. Inclined prism

The second type of this spatial figure is the oblique prism. Its side walls are parallelograms. They usually lie in planes that are not perpendicular to the postures.


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1.3. Archimedean prism

An Archimedean prism, otherwise known as a prism, is a normal prism whose base edge is the same length as its height. Apart from the antiprisms, Archimedean prisms form one of the two infinite series of semi-rectangular polyhedra.

2. Elements of the prism

Each prism is made up of fixed elements such as:

  • the basics;
  • base edge;
  • side edge;
  • side wall;
  • top.

3. Formula for the volume of a prism

To calculate the volume of the prism, we use the formula:

V = P x H.


V is the volume, P is the base area, and H is the height.

4. Formula for the total area of ​​a prism

To calculate the total area of ​​a prism, we use the formula:

Pc = 2 Pp + Pb


Pc is the total area, Pp is the base area, and Pb is the lateral area (the sum of half of all side walls).

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