B. Count the number of triangles.

INSIGHT

Пошаговое решение:

1. Examine the given figure, which is a large triangle divided by several internal lines.
2. Identify the smallest individual triangles. There are 4 such triangles at the bottom.
3. Look for triangles formed by combining two smaller shapes. There are 3 such triangles, each formed by combining two of the smallest triangles.
4. Look for triangles formed by combining three smaller shapes. There are 2 such triangles.
5. Look for triangles formed by combining four smaller shapes. There is 1 such triangle.
6. Look for triangles formed by combining five smaller shapes. There are no such triangles.
7. Look for triangles formed by combining six smaller shapes. There are no such triangles.
8. Consider the largest triangle encompassing the entire figure. This is 1 triangle.
9. Let's count systematically:
   • Smallest triangles (1 unit): 4
   • Triangles made of 2 units: 3
   • Triangles made of 3 units: 2
   • Triangles made of 4 units: 1
10. Total number of triangles = 4 + 3 + 2 + 1 = 10.
11. Let's verify by counting directly:
    • Smallest, single triangles: 4
    • Triangles formed by two adjacent small triangles: 3
    • Triangles formed by three adjacent small triangles (two bottom + one above): 2
    • The largest triangle encompassing all: 1
12. Total = 4 + 3 + 2 + 1 = 10.
13. Another way to count:
    • Triangles pointing upwards:
      • Smallest: 4
      • Medium (composed of 2 small): 3
      • Larger (composed of 3 small): 2
      • Largest (whole figure): 1
14. Total = 4 + 3 + 2 + 1 = 10.
15. Let's use a formula for a triangle divided by n parallel lines. In this case, it's not parallel lines, but lines from a vertex to the base.
16. If a triangle has 'n' lines drawn from one vertex to the opposite side, dividing it into 'n+1' segments, the number of triangles formed is (n+1)(n+2)/2. Here, the base is divided into 4 segments, so n=3 lines from the vertex. This formula does not apply directly as the lines are not all from one vertex to the base, and there are horizontal divisions.
17. Let's stick to direct counting.
18. Smallest triangles: 4
19. Triangles formed by 2 smallest: 3
20. Triangles formed by 3 smallest: 2
21. The whole triangle: 1
22. Total = 4+3+2+1 = 10.