Triangle count refers to the tessellated result of the final mesh, required by graphics cards to draw geometry, not necessarily your mesh polygons.
A four sided face will be made up of two triangles, even though no three sided faces are present in your model.
To find all three sided faces faces in one mesh, while in Edit Mode select one of the triangles, the use the Select Similar operator Shift + G > Polygon Sides.
Or If one can't easily be found, do the inverse process, select a quad, then invert selection with Ctrl + i.