Systematic Approach to Counting Triangles

To find the total number of triangles in the given figure without missing any or counting some twice, the best method is to count them based on how many smaller components they are composed of.

1. Triangles Made of a Single Component

First, we count the smallest, individual triangles that are not subdivided further. If you look closely, you can identify 6 such triangles.

2. Triangles Made of Two Components

Next, we look for triangles that are formed by combining two of the smaller adjacent components. There are 5 such triangles in the figure.

3. Triangles Made of Three Components

We then look for larger triangles formed by the combination of three smaller components. There are 2 such triangles (one forming the larger left section and one forming the larger right section).

4. Triangles Made of Six Components

Finally, the entire outer boundary of the figure itself forms one large triangle, which is composed of all the smaller pieces. This gives us 1 more triangle.

Total Calculation

To find the total number of triangles, we sum the counts from each category:

Total = (1-component triangles) + (2-component triangles) + (3-component triangles) + (6-component triangles)

Total = 6 + 5 + 2 + 1 = 14

Therefore, there are 14 triangles in the picture.