ANS:A - 44 triangles, 10 squares

The figure may be labelled as shown. Triangles : 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. Squares : The squares composed of two components are HIOL, IEJO, JFKO and KGLO i.e. 4 in number. The squares composed of four components are AEOH, EBFO, OFGC and HOGD i.e.4 in number. There is only one square EFGH which is composed of eight components. There is only one square ABCD which is composed of sixteen components. Total number of squares in the figure = 4 + 4 + 1 + 1 = 10.