In a standard geometric configuration consisting of a large master triangle divided by internal intersecting line cevians from two vertices creating a grid of internal bounded elements, what is the maximum number of distinct embedded triangles contained in such a figure?

- A
- B
- C
- D
Solution & Step-by-step Explanation
Let us count the triangles systematically by grouping them by the number of individual smaller component regions they contain:
1. Single-region independent triangles: Counting the smallest individual triangular spaces inside the split sections yields small triangles.
2. Double-region combined triangles: Combining pairs of adjacent regions sharing an internal edge gives additional triangles.
3. Triple-region combined triangles: Combining groups of three adjacent structural compartments yields intermediate triangles.
4. Complete outer triangle: The full master triangle itself adds final boundary triangle.
Adding these individual counts together:
1. Single-region independent triangles: Counting the smallest individual triangular spaces inside the split sections yields small triangles.
2. Double-region combined triangles: Combining pairs of adjacent regions sharing an internal edge gives additional triangles.
3. Triple-region combined triangles: Combining groups of three adjacent structural compartments yields intermediate triangles.
4. Complete outer triangle: The full master triangle itself adds final boundary triangle.
Adding these individual counts together: