question_answer

How many triangles are there in the figure given?

A)  10                                         

B)  12

C)  14                                         

D)  16

Correct Answer: C

Solution :

The figure may be labelled as shown. The simplest triangles are ABJ, ACJ, BDH, DHF, CIE and GIE i.e. 6 in number. The triangles composed of two components each are ABC, BDF, CEG, BHJ, JHK, JKI and CJI i.e. 7 in number. There is only one triangle JH1 which is composed of four components. Thus, there are \[\text{6}+\text{7}+\text{1}=\text{14}\] triangles in the given figure.