How Many Triangles?

A Method to count:

Assume first that the smallest triangles are of a unit length. Note that every possible triangle are equilateral.

Now, count as follows:

(i) How many triangles are of a unit length?
9 unit-length triangles

(ii) How many triangles are of two unit lengths?
3 two-unit-length triangles

(iii) How many triangles are of three unit lengths? 1 three-unit-length triangle

So, in total there are:

9 + 3 + 1 = 13 (Answer) triangles in all.