question_answer

Find the number of triangles in the diagram given below.  [UPPSC (RO) 2014]

A) 32                                

B) 31  

C) 30                                

D) 29

Correct Answer: A

Solution :

In order to count the triangles, we first name the vertices.

Now, counting can be observed.

In \[\Delta ADE,\,\,\Delta AOD,\,\,\Delta OAN,\,\,\Delta NAM,\,\,\Delta MAE,\]

\[\Delta DAN,\,\,\Delta OAM,\,\,\Delta NAE,\,\,\Delta DAM,\,\,\Delta OAE,\,\,\Delta DAE=10\]Similarly,\[\Delta BDF\]and\[\Delta CEF\]will have 10 and 10 triangles.\[\Delta DEF\]and\[\Delta ABC\]will count 2, hence total \[10+10+10+2=32\]