To know how many edges a hexagonal prism has, you must know the meaning of "edge", "prism" and "hexagonal". The first two concepts are general definitions, and the third concept has to do with the shape of the geometric figure.
When talking about hexagonal, mention is made of a hexagon (polygon). The prefix "hexa" indicates that the polygon has six sides.
An edge is an edge of an object. Geometrically, it is a line that connects two consecutive vertices of a geometric figure.
A prism is a geometric figure bounded by two bases that are parallel and equal polygons and their lateral faces are parallelograms.
In the following image, it can be seen that the lateral faces of a hexagonal prism can be rectangles, but they can also be parallelograms.
According to the type of parallelograms, premiums can be classified into two types: straight and oblique.
How to count the edges of a hexagonal prism?
The number of edges that a hexagonal prism will have will not change whether it is a straight or oblique prism. Also, the number of edges does not depend on the length of the sides.
Counting the edges of a hexagonal prism can be done in several ways. Two ways are described below:
1- Decompose the prism
One way to count the edges is by decomposing the hexagonal prism into its two bases and its lateral faces. In this way, two hexagons and a parallelogram with five interior lines are obtained.
Each hexagon has six edges, therefore the prism will have more than 12 edges.
At first glance it is thought that the parallelogram contains nine edges (seven vertical and two horizontal). But it is convenient to stop and analyze this case.
When the parallelogram is bent to form the prism, it can be seen that the first line on the left will join the last line on the right, whereby both lines represent a single edge.
But what about the two horizontal lines?
When all the pieces are put together again, the horizontal lines will join, each one, with the six edges of each hexagon. For this reason, counting them separately would be a mistake.
So the parallelogram contains six edges of the prism which, together with the 12 edges counted at the beginning, gives a total of 18 edges.
2.- Projecting each edge
Another way, much easier to count the edges, is using the fact that the bases of the hexagonal prisms are hexagons, so each base has six edges.
On the other hand, from each vertex of a hexagon a single edge is projected to the corresponding vertex of the other hexagon; that is, there are six edges that join one base to the other.
By adding all the edges, you get a total of 18 edges.
conclusion
It can be shown that the number of edges of a prism is equal to three times the number of edges that the polygon that forms it has.
Therefore, a pentagonal prism will have 3 * 5 = 15 edges, a heptagonal prism will have 3 * 7 = 21 edges and so it can be applied to any prism.
References
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