Question

Q18. Count the number of triangles in the following figure.

• A. (a) 27
• B. (b) 26
• C. (c) 24
• D. (d) 23

Answer 1

The correct option is A

(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.