The figure may be labelled as shown.
The simplest triangles are ABF, BIC, CIH, GIH, FGE and AFE i.e. 6 in number.
The triangles composed of two components each are ABE, AGE, BHF, BCH, CGH and BIE i.e. 6 in number.
The triangles composed of three components each are ABH, BCE and CDE i.e. 3 in number.
Hence, the total number of triangles in the figure = 6 + 6 + 3 = 15.