Question

Count the number of triangles in the following figure.

• A. 27
• B. 26
• C. 24
• D. 23

Answer 1

The correct option is A 27


Label the vertices of the figure as shown: The simplest triangles are GKL, MHN, DLJ, DMJ, QRE, OPF PIA, and IRA, i.e., 8. The triangle having 2 components each are BDO, CDQ, DLM, PRA, KFI, NEI, HJI, GJI, DKI, and DNI i.e., 10. The triangles having 4 components each are DIE, DFI, DOA, DQA, and DHI, i.e., 5. The triangle having 6 components each are DCA and DBA , i.e., 2. DEF is the only triangle having 8 components. ABC is the only triangle having 12 components. Thus, there are 8+10+5+2+1+1=27 triangle in the figure.