Counting sequentially......
If there are no internal lines, 1 triangle.
Draw the vertical line, 2 new triangles.
Draw the line from the left vertex to the right side, 5 new triangles.
Draw the line from the right vertex to the left side, 6 new triangles.
Draw the line from the left side to the mid-base, 7 new triangles.
Draw the line from the right side to the mid-base, 7 new triangles.
Total 28.