question_answer

How many triangles are there in the following figure?

A)  12                         

B)         13

C)  14                         

D)         15

Correct Answer: D

Solution :

The figure may be labelled as shown. The simplest triangles are ABF, BIC, CIH, GIH, FGE and AFE i.e. 6 in number. The triangles composed of two components each are ABE, AGE, BHF, BCH, CGH and BIE i.e. 6 in number. The triangles composed of three components each are ABH, BCE and CDE i.e. 3 in number. Hence, the total number of triangles in the figure = 6 + 6 + 3 =15.