How many triangles are there in the figure given below?

To find the total number of triangles in the given figure, we can divide the figure into two main independent sections: the upper-left triangular section and the lower-right square section. Since these two sections only touch at a single vertex, no new triangles are formed by combining them.

Step 1: Count the triangles in the upper-left section
Let the topmost vertex of this section be T. The vertical line on the right and the sloping line on the left form a series of nested triangles, capped by horizontal parallel lines.
From top to bottom, each horizontal line forms a new triangle with the vertex T:

• 1. The triangle formed by the first (topmost) horizontal line.
• 2. The triangle formed by the second horizontal line.
• 3. The triangle formed by the third horizontal line.
• 4. The triangle formed by the fourth (bottom-most) horizontal line of this section.

Step 2: Count the triangles in the lower-right square section
By systematically identifying the individual non-overlapping triangles and the larger combined triangles within the partitioned square, we find:

• There are exactly 6 triangles in this square section.

Step 3: Calculate the total number of triangles
Summing the triangles from both sections:
$\text{Total Triangles}=4+6=10$

Therefore, the correct option is 10.