- Ways to count the edges of a pentagonal prism
- 1- First way
- 2- Second way
- Other types of prism
- Triangular prism
In order to count how many edges a pentagonal prism has, the concepts "edge" (edge of an object), "prism" (geometric figure), and "pentagonal" (relative to the shape of a geometric figure) must be understood.
When talking about pentagonal, the first thing to think about is that the prefix «penta» indicates that the figure must have five sides. Therefore, the figure should have a shape similar to that of a pentagon.
Pentagonal Prism
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, which are equal and parallel polygons, and whose lateral faces are parallelograms.
In the image shown at the beginning, the lateral faces of the pentagonal prism are rectangles. This is only a particular case, because the definition indicates that its lateral faces are parallelograms.
This allows prisms to be classified as "straight" and "oblique".
To know how many edges a pentagonal prism has, the type of prism with which you are working does not matter. Be it straight or oblique, the number of edges will not change.
Ways to count the edges of a pentagonal prism
1- First way
Since the bases of pentagonal prisms are pentagons, then each base has five edges.
On the other hand, from each vertex of a pentagon an edge is projected to the corresponding vertex of the other pentagon; that is, there are five edges that join one base to the other.
By adding all the edges we get a total of 15 edges.
2- Second way
Another way to count the edges is by decomposing the pentagonal prism into its two bases and its lateral faces. This will give two pentagons and a parallelogram with four interior lines.
Each pentagon has five edges. On the other hand, at first glance one could make the mistake of saying that the parallelogram contains eight edges (six vertical and two horizontal). But this reasoning must be better analyzed.
If all vertical lines are counted, it is notable 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 five edges of each pentagon. For this reason, counting them separately would be a mistake.
So the parallelogram contains five edges of the prism which, together with the 10 edges counted at the beginning, gives a total of 15 edges.
Other types of prism
Triangular prism
These are prisms in which the bases are triangles, and the number of edges is 9.
Original text
Contribute a better translation
. Matemáticas: un enfoque de resolución de problemas para maestros de educación básica. López Mateos Editores.</li>
<li>Fregoso, R. S., & Carrera, S. A. (2005). Matemáticas 3. Editorial Progreso.</li>
<li>Gallardo, G., & Pilar, P. M. (2005). Matemáticas 6. Editorial Progreso.</li>
<li>Gutiérrez, C. T., & Cisneros, M. P. (2005). Curso de Matemáticas 3º. Editorial Progreso.</li>
<li>Kinsey, L., & Moore, T. E. (2006). Symmetry, Shape and Space: An Introduction to Mathematics Through Geometry (illustrated, reprint ed.). Springer Science & Business Media.</li>
<li>Mitchell, C. (1999). Dazzling Math Line Designs (Illustrated ed.). Scholastic Inc.</li>
<li>R., M. P. (2005). Yo dibujo 6º. Editorial Progreso.</li>
</ol>
<!-- google_ad_section_end -->
</div>
</article>
<div class=)