Question

How many triangles are there in the figure given below?

• A. $21$
• B. $19$
• C. $18$
• D. $20$

Answer 1

The correct option is B $19$


Simplest triangles are ABG, BHG, FGH, AGF, HCI, CID, DIE, HIE and BCH, i.e., $9$ in number.

The triangles composed of two components each are ABH, BHF, HFA, FAB, HCD, CDE, DEH and EHC, i.e., $8$ in number.

The triangles composed of three components each are BCE and BCF, i.e., $2$ in number.

Total number of triangles in the figure $=9+8+2=19.$