How many edges are in a hexagonal prism?
Understand the Problem
The question is asking for the number of edges in a hexagonal prism, a 3-dimensional geometric shape with hexagonal bases. To determine this, we can count the edges of the two hexagonal bases and the edges connecting the corresponding vertices of the bases.
Answer
$18$
Answer for screen readers
The total number of edges in a hexagonal prism is $18$.
Steps to Solve
- Count the edges of the hexagonal bases
A hexagon has 6 edges. Since a hexagonal prism has two hexagonal bases, we multiply the number of edges in one hexagon by 2:
$$ 6 \text{ edges/hexagon} \times 2 \text{ hexagons} = 12 \text{ edges} $$
- Count the edges connecting the bases
In addition to the edges of the bases, we must also account for the edges that connect the corresponding vertices of the two hexagons. Since there are 6 vertices on each hexagon, there will be 6 edges connecting them:
$$ 6 \text{ edges connecting vertices} $$
- Calculate the total number of edges
Now, we can find the total number of edges in the hexagonal prism by adding the edges from the bases and the edges connecting the bases:
$$ 12 \text{ edges from bases} + 6 \text{ edges connecting} = 18 \text{ edges} $$
The total number of edges in a hexagonal prism is $18$.
More Information
A hexagonal prism is an excellent example of a polyhedron, which is a solid figure with many plane faces. Understanding the number of edges can help in discussions about surface area, volume, and other geometric properties.
Tips
- Confusing the number of edges in a shape by not accounting for the edges connecting the two bases. Always remember to count edges from both the bases and the height connections.
- Forgetting to multiply the edges of one base by the number of bases.
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