Question

Triangle Decomposition of Polygons Quick Check
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Question
Use the image to answer the 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.

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.

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.
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Answer 1

The correct answer is:

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

In a hexagon, the number of triangles formed when a vertex connects to non-adjacent vertices is indeed \( n - 2 \), where \( n \) is the number of sides of the polygon. Since a hexagon has 6 sides, \( 6 - 2 = 4 \), confirming that the decomposition into 4 triangles is accurate.