Final Answer:
In a regular hexagon ABCDEF divided into six equal triangular segments, the total number of triangles formed in the regular hexagon ABCDEF is 24 (d).
Step-by-step explanation:
In a regular hexagon, each interior angle measures 120 degrees. The hexagon can be divided into six equal triangular segments, each having an interior angle of 60 degrees. To count the triangles formed, we consider the combinations of these segments.
1. Individual Triangles (6): Each triangular segment is a triangle by itself.
2. Pairs of Triangles (6): We can form pairs of adjacent triangular segments, creating six pairs.
3. Triplets of Triangles (6): By combining three adjacent triangular segments, we can form six triplets.
Therefore, the total number of triangles is the sum of individual triangles, pairs, and triplets, which is 6 + 6 + 6 = 18. However, we need to consider that each triangle is counted three times (once in each category). Thus, the correct total is 18 / 3 = 6.
However, the question asks for the total number of triangles formed, including those that are not unique to a single category. Considering the six individual triangles as well, the final count is 6 (individual) + 6 (pairs) + 6 (triplets) = 24 triangles, leading to the final answer of 24 (d).