How many triangles are there in the given figure?

The correct answer is 13.

To find the total number of triangles in the given figure, we can systematically count them region by region:

1. Small top-left overlapping square structure:

- Looking at the top-left square that has an inscribed diamond/rotated square, the corners form 4 small triangles.
- The square inside that overlaps with the main grid corner also has diagonal lines forming triangles.
- Counting the distinct individual small triangular regions in this top-left region yields 6 triangles.

2. Upper-middle section:

- There is a V-shaped branch/slanting lines near the top border attached to a vertical line, forming 2 triangles.

3. Right side section:

- On the upper-right area within the outer square, diagonal lines cut across forming 2 triangles.

4. Bottom-left corner section:

- At the very bottom-left corner of the main square, a single slanting line cuts the corner to form 1 triangle.

5. Center-bottom section:

- In the lower central grid area, a diagonal line divides a small square section, contributing 2 triangles.

Total Count:

Adding all the individual triangular regions together:

$6+2+2+1+2=13$

Thus, there are a total of 13 triangles in the given figure.