A prism is a polyhedron whose two bases are congruent (equal) polygons that lie in parallel planes. The lateral faces are flat faces that form parallelograms with sides in common with these polygons.
These parallelograms are called the lateral faces of the prism, and the two remaining polygons are called its bases.
Characteristics of prisms
Below I show you 10 characteristics that define a prism:
- Congruent bases : Prisms have two identical bases located in parallel planes.
- Lateral faces : The lateral faces are parallelograms or rectangles , depending on the type of prism.
- Lateral edges : All lateral edges are equal to each other and parallel .
- Volume : The volume of a prism is calculated as the product of the area of the base and the height of the prism: V=A base ⋅h.
- Surface area : The total area of the prism is the sum of the areas of all its faces: A total = Alateral +2⋅A base
- Lateral surface area : The lateral area of a prism can be calculated using the formula:
A lateral =P⋅l
In a right prism:
A lateral =P⋅h - Geometric properties : The lateral edges are perpendicular to any perpendicular section.
- Angles of perpendicular section : The angles of a perpendicular section correspond to the dihedral angles formed at the lateral edges.
- Perpendicularity of lateral faces : The lateral faces are perpendicular to any cross section.
- Axis of symmetry : The center of the bases coincides with the axis of symmetry of the prism.
Examples of prisms
Here are some examples of prisms, including everyday applications:
Prisma triangular
This prism has triangles as bases. It is one of the simplest and easiest shapes to visualize.
Everyday examples include a gable roof or a ramp to improve accessibility for wheelchair users. These structures have the shape of a triangular prism due to their triangular base.
Quadrangular prism
This prism has quadrilaterals as bases, and if the bases are square, the prism is particularly symmetrical, forming a regular structure.
This is a geometric pattern that is very common in our daily lives. For example, a shoe box is a common representation of these three-dimensional figures.
Prisma pentagonal
This prism has pentagons as bases, which gives it a more complex and less common structure compared to other prisms.
Some buildings with modern architectural design (such as the Pentagon in the United States) have a base that resembles a pentagonal prism.
Types of prisms
Straight prism
A right prism is one whose main characteristic is that its lateral edges are perpendicular to the bases.
This means that the lines connecting the bases are perpendicular to the surfaces of the bases. As a result, the lateral faces of a right prism are always rectangles. This property gives the prism a simpler and more symmetrical structure, with a constant height between the two bases.
Prisma regular
A regular prism is a specific type of right prism in which, in addition to having the lateral edges perpendicular to the bases, the bases are regular polygons.
This means that the bases have all sides and angles equal, as in a regular triangular prism (with equilateral triangular bases) or a regular hexagonal prism (with hexagonal bases). The lateral faces are identical rectangles, since all lateral edges have the same length and are aligned evenly.
Oblique prism
An oblique prism is characterized because the lateral edges are not perpendicular to the bases.
According to this definition, instead of being straight, the lateral edges are inclined, which causes the lateral faces of the prism to not be rectangles, but inclined parallelograms.
The base remains parallel to itself, but the side faces acquire an inclination, which results in a less symmetrical shape compared to the right prism.
Differences between prisms and pyramids
The differences between prisms and pyramids lie mainly in their geometric structure.
One of the key differences is the number of bases. While prisms have two congruent bases lying in parallel planes, pyramids have a single base from which all their lateral faces extend to meet at a single point or vertex known as the apex.
Another notable difference is found in the lateral faces. In prisms, the lateral faces are either parallelograms (in oblique prisms) or rectangles (in right prisms), which connect corresponding sides of the two bases. In contrast, the lateral faces of pyramids are triangles that share a common vertex.
In addition, pyramids usually have a smaller number of faces, edges and vertices compared to prisms, since their design is simpler and more compact, due to the absence of a second base.