Question

How many triangles are there in the figure given below?

• A. $36$
• B. $44$
• C. $52$
• D. $47$

Answer 1

The correct option is B $44$


The simplest triangles are AEI, EOI, OHI, HAI, EBJ, BFJ, FOJ, OEJ, HOL, OGL, GDL, DHL, OFK, FCK, CGK, and GOK i.e., $16$ in number.

The triangles composed of two components each are HAE, AEO, EOH, OHA, OEB, EBF, BFO, FOE, DHO, HOG, OGD, GDH, GOF, OFC, FCG, and CGO i.e., $16$ in number.

The triangles composed of four components each are HEF, EFG, FGH, GHE, ABO, BCO, CDO, and DAO i.e., $8$ in number.

The triangles composed of eight components each are DAB, ABC, BCD, and CDA i.e., $4$ in number.

Hence, total number of triangles in the figure $=16+16+8+4=44.$