How many triangles are there in the following figure?

Let us label the vertices of the main triangle as $A$ at the top, $B$ at the bottom-left, and $C$ at the bottom-right. The line from the top vertex $A$ meets the base $BC$ at point $D$. Lines drawn from the vertex $B$ intersect the line segment $AD$ and side $AC$.
Counting the triangles systematically by combining smaller regions:

* Triangles consisting of 1 single region: 5 triangles
* Triangles consisting of 2 combined regions: 4 triangles
* Triangles consisting of 3 combined regions: 2 triangles
* The largest main triangle ($△ABC$): 1 triangle

Adding these together:

$$5+4+2+1=12\text{ triangles}$$

Therefore, the total number of triangles in the figure is 12.