How many triangles are there in the given figure?

In figure 1 = 

Outer triangle=1+1+1+1 =4 triangles

In inner square = 8 triangles ( by manual counting)

therefore there are 12 triangles in figure 1

In figure 2 = 

Outer triangle=1+1+1+1 =4 triangles

In inner square = 8 triangles ( by manual counting)

therefore there are 12 triangles in figure 2

So, total triangles = 24