Count the number of triangles given in the figure below :

We can see that this figure is symmetric from the middle horizontally and vertically.

Lets first see the top half part vertically, we can see that we have 4 triangular fragments. 

So smallest triangles present here are 4 

Next we can combine 2 adjacent fragments to get 3 bigger triangles, similarly we can combine 3 adjacent fragments to get 2 even bigger triangles and finally we can combine all fragments to get the largest triangle in this selection.

Therefore vertical half part has 10 triangles and due to symmetry in figure bottom half will also have 10 triangles.

Now, If we look the figure horizontally these are total of 4 more triangles possible.

Thus total count is : 10+10+4 = 24

Hence option D is correct.