Find the number of triangles in the given figure.

Step-by-step solution

The figure may be labelled as shown. The simplest triangles are GLK, DLJ, DJM, HMN, QRE, IRA, IPA and FPO i.e. 8 in number. The triangle having two components each are BDO, CDQ, DLM, PRA, KFI, NEI, HJI, GJI, DKI and DNI i.e. 10 in number. The triangles having four components each are DIE, DFI, DOA, DQA and GHI i.e. 5 in number. The triangles having six components each are DCA and DBA i.e. 2 in number. DEF is the only triangle having eight components. ABC is the only triangle having twelve components. Thus, there ar