Counting

1 x 1 triangles: 3

1 x 2 triangles: 2

1 x 3 triangles: 1

2 x 1 triangles: 3

2 x 2 triangles: 2

2 x 3 triangles: 1

3 x 1 triangles: 3

3 x 2 triangles: 2

3 x 3 triangles: 1

4 x 1 triangles: 3

4 x 2 triangles: 2

4 x 3 triangles: 1

 

Now, add them up...