Find the number of triangles in the given figure.

Step-by-step solution

The figure may be lebelled as shown. The simplest triangles are AHL, LHG, GHM, HMB, GMF, BMF, BIF, CIF, FNC, CNJ, FNE, NEJ, EKJ and JKD i.e. 14 in number. The triangles composed of two components each are AGH, BHG, HBF, BFG, HFG, BCF, CJF, CJE, JEF, CFE and JED i.e. 11 in number. The triangles composed of four components each are ABG, CBG, BCE and CED i.e. 4 in number. ∴ Total number of triangles in the given figure = 14 + 11 + 4 = 29. Hence, option C is correct.