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Question

An illustration shows a bee on top of a square honeycomb. The cells inside the honeycomb are shaped like hexagons. In one of the cells, lines connect the vertex at the top left to the three non-adjacent vertices.

Is this the correct decomposition of a honeycomb shaped like a hexagon into n−2 triangles?

(1 point)
Responses

No, this is not the correct decomposition because the decomposition is 4 equal-sized triangles.
No, this is not the correct decomposition because the decomposition is 4 equal-sized triangles.

No, this is not the correct decomposition because the decomposition is 4 triangles.
No, this is not the correct decomposition because the decomposition is 4 triangles.

Yes, this is the correct decomposition because the decomposition is 6 triangles.
Yes, this is the correct decomposition because the decomposition is 6 triangles.

Yes, this is the correct decomposition because the decomposition has n−2=6−2=4 triangles.
Yes, this is the correct decomposition because the decomposition has n minus 2 equals 6 minus 2 equals 4 triangles.
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Answer 1

To determine if the decomposition of the hexagonal honeycomb cell is correct, we need to consider how many vertices the hexagon has and how the triangles are formed.

A regular hexagon has 6 vertices. The standard formula for decomposing a polygon into triangles is that for a polygon with \( n \) vertices, it can be decomposed into \( n - 2 \) triangles. Therefore, for a hexagon (\( n = 6 \)), it can be decomposed into:

\[ n - 2 = 6 - 2 = 4 \text{ triangles} \]

The description states that lines are drawn from one vertex to three non-adjacent vertices, which is a common method for triangulating a hexagon.

Now, examining the options:

• The decomposition creates 4 triangles, which aligns with our calculation \( n - 2 = 4 \).
• The other options that suggest a decomposition of 6 triangles are incorrect, as they misinterpret the relationship.

Thus, the correct response is:

Yes, this is the correct decomposition because the decomposition has n−2=6−2=4 triangles.