question_answer

Find the number of triangles in the given figure.

A)  12                  

B)  24

C)  26                  

D)  18

Correct Answer: D

Solution :

[d] The figure may be labeled as shown.

The simplest triangles are AHB, GHI, BJC, GFE, GIE, IJE, CEJ and CDE i.e. 8 in number.

The triangles composed of two components each are HEG, EEC, HBE, JGE and ICE i.e. 5 in number.

The triangles composed of three components each are FHE, GCE and BED i.e. 3 in number.

There is only one triangle i.e. AGC composed of four components.

There is only one triangle i.e. AFD composed of nine components.

Thus, there are 8+5+3+1+1=8 triangles in the given figure.