Question

The total number of triangles in the given figure is

• A. $19$
• B. $17$
• C. $21$
• D. $23$

Answer 1

The correct option is C $21$


The simplest triangles are KJN, KJO, CNB, OEF, JIL, JIM, BLA and MFG i.e. $8$ in number.

The triangles composed of two components each are CDJ, EDJ, NKO, JLM, JAH and JGH i.e. $6$ in number.

The triangles composed of three components each are BKI, FKI, CJA and EJG i.e. $4$ in number.

The triangles composed of four components each are CDE and AJG i.e. $2$ in number.

The only triangle composed of six components is BKF.

Thus, there are $8+6+4+2+1=21$ triangles in the given figure.