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Relax 2025-04-10 10:50:08

How many triangles?

Let's count the number of triangles in the image:

We can see that the main shape is a large triangle divided by horizontal and vertical lines:

  1. There are 3 horizontal lines dividing the large triangle into 4 levels.

  2. There are 2 vertical lines, which divide each level into 3 parts (creating multiple smaller triangles).

  3. Overall, the shape contains many small triangles, both individual and combinations of smaller ones.

Counting:

Level 1 (top):

  • 1 small triangle.

Level 2:

  • 2 small triangles (left and right).

  • Plus 1 larger triangle formed by combining the whole level → 3 triangles in total.

Level 3:

  • 3 small triangles (left, center, right).

  • 2 medium triangles formed by combining two small ones.

  • 1 large triangle from the entire level → 6 triangles in total.

Level 4 (bottom):

  • 3 small triangles.

  • 3 medium triangles (each combining two small ones).

  • 1 large triangle from the full level → 7 triangles in total.

Total triangles from each level:

  • Level 1: 1

  • Level 2: 3

  • Level 3: 6

  • Level 4: 7

Additionally, triangles formed by combining multiple levels:

  • Level 1 + 2: 1

  • Level 2 + 3: 2

  • Level 3 + 4: 3

  • Level 1 to 3: 1

  • Level 2 to 4: 1

  • Whole large triangle: 1

Total combined triangles: 9

Final Total:

1 (level 1) + 3 (level 2) + 6 (level 3) + 7 (level 4) + 9 (combinations) = 26 triangles

✅ Answer: 26 triangles

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