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Question
Find the number of triangles in the figure.
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Solution
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, BGO, 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.
Total number of triangles in the figure = 16 + 16 + 8 + 4 = 44
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, BGO, 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.
Total number of triangles in the figure = 16 + 16 + 8 + 4 = 44
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