The figure may be labelled as shown.
The simplest triangles are AFJ, FJK, FKB, BKG, JKG, JGC, HJC, HIJ, DIH, DEI, EIJ and AEJ i.e. 12 in number.
The triangles composed of two components each are JFB, FBG, BJG, JFG, DEJ, EJH, DJH and DEH i.e. 8 in number.
The triangles composed of three components each are AJB, JBC, DJC and ADJ i.e. 4 in number.
The triangles composed of six components each are DAB, ABC, BCD and ADC i.e. 4 in number.
Thus, there are 12 + 8 + 4 + 4 = 28 triangles in the figure.