question_answer

Identify the number of triangles in the figure given.

A)  22                                         

B)  24

C)  26                                         

D)  28

Correct Answer: D

Solution :

We may label the figure as shown. The simplest triangles are AGH, GFO, LFO, DJK, EKP, PEL and IMN i.e. 7 in number. The triangles having two components each are GFL, KEL, AMO, NDP, BHN, CMJ, NEJ and HFM i.e. 8 in number. The triangles having three components each are IOE, IFP, BIF, and CEI i.e. 4 in number. The triangles having four components each are ANE and DMF i.e. 2 in number. The triangles having five components each are FCK, BGE and ADL i.e. 3 in number. The triangles having six components each are BPF, COE, DHF and AJE i.e. 4 in number. \[\therefore \]Total number of triangles in the figure =7 + 8 + 4 + 2 + 3 + 4 = 28.