THE 5 MAIN CHARACTERISTICS OF A PENTAGONAL PRISM - MATHS - 2024

The characteristics of a pentagonal prism are those details that differentiate it from other geometric figures.

Furthermore, these characteristics also serve to separate the pentagonal prisms into several disjoint sets, that is, they allow a distinction to be made between the same pentagonal prisms.

The characteristics will not depend on the size of the prism or its volume, that is, the prisms are not classified by the magnitude of their sides.

But if they can be classified, for example, observing if all the sides of the pentagon measure the same or not.

Definition of prism

First it is important to know the definition of a prism.

A prism is a geometric body such that its surface is made up of two bases that are equal and parallel polygons, and five lateral faces that are parallelograms.

Characteristics of a Pentagonal Prism

Among the characteristics of a pentagonal prism are:

1.- Number of bases, faces, vertices and edges

The number of bases of a pentagonal prism is 2 and these are pentagons.

A pentagonal prism has five sides that are parallelograms. In total, the pentagonal prism has seven faces.

The number of vertices is equal to 10, five for each pentagon. The number of edges can be calculated with the Euler formula which says:

c + v = a + 2, where "c" is the number of faces, "v" is the number of vertices and "a" is the number of edges. Thus, 7 + 10 = a + 2, equivalently, a = 17-2 = 15.

Therefore, the number of edges is 15.

2.- Its bases are Pentagons

The two bases of a pentagonal prism are pentagons. This differentiates it from other prisms such as a triangular prism, a rectangular prism or a hexagonal prism, among others.

3.- Regular and Irregular

If the lengths of the 5 sides of the pentagon are all equal, then the pentagon is said to be regular; otherwise it is said to be irregular.

If the pentagons are regular (irregular), then the pentagonal prism is said to be regular (irregular).

Therefore, pentagonal prisms can be classified into Regular and Irregular.

4.- Straight or Oblique

If the parallelograms that form the five lateral faces are rectangles then the pentagonal prism is called a right pentagonal prism. Otherwise, it is called an oblique pentagonal prism.

In other words, if the angle formed between the lateral faces and the bases is a right angle, then the prism is called a right prism; otherwise it is called oblique.

5.- Concave and Convex

A polygon is called concave when one of its interior angles measures more than 180º, and it is called convex when all its interior angles measure less than 180º.

It can also be said that a polygon is convex if, given any pair of points within it, the line that joins both points is completely contained within the polygon.

Therefore, if the chosen pentagon is concave, then the pentagonal prism is called concave. If, on the contrary, the chosen pentagon is convex, then the pentagonal prism will be called convex.

Observation

The calculation of the volume of a pentagonal prism depends on whether it is straight or oblique, and whether it is regular or irregular.

In particular when the pentagonal prism is straight and regular, it is much easier to calculate the volume.

References

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