question_answer

How many triangles are there in the figure given?

A)  18                                         

B)  20

C)  28                                         

D)  34

Correct Answer: C

Solution :

The figure may be labelled as shown below: The simplest triangles are AEI, AIH, BEJ, BJF, CFK, CKG, DGL, DLH, EOJ, FOJ, FOG, LOG, HOL and HOE i.e. 14 in number. The triangles composed of two components each are EAH, FBE, BEO, EOF, BFO, FCG, GDH, HOD, HOG, and GOD i.e. 10 in number. The triangles composed of three components each are EFH, EHG, FGH and EFG i.e. 4 in number. Thus, there are \[\text{14}+\text{1}0+\text{4}=\text{28}\]triangles in the given figure.