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.

Question

GPT-4o mini · Answer

To determine whether the decomposition of a hexagon-shaped honeycomb into triangles is correct, we need to understand the properties of a hexagon and its decomposition into triangles.

A regular hexagon has 6 sides (n = 6). According to the formula mentioned, to decompose a convex polygon with n sides into triangles, the number of triangles formed is n - 2.

For a hexagon (n = 6):

The formula gives us: 6 - 2 = 4 triangles.

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

The other responses that claim the decomposition is 6 triangles are incorrect because that applies to a hexagon with a different decomposition method, not the straightforward triangulation method that results in 4 triangles.

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