After labelling the figure, we get the following,

• Simplest triangles JBO, BKO, KDO, DFO, FGO, GHO, HIO, IJO, ABJ, BCK, CKD and DEF (12)
• Triangles with two components each IBO, BDO, DGO, GIO, ABO, CBD and DEO (7)
• Triangles with four components IBD, BDG, DGI, GIB, ACO, and COE (6)
• Triangle with eight components is ACE (1)

Total number of triangles in the figure is 12 + 7 + 6 + 1 = 26

Also we need to count the number of squares in this figure,

• Squares with two components each BKOJ, KDFO, OFGH, and JOHI (2)
• Square composed of four components is CDOB (1)
• Square composed of eight components is BDGI (1)

Total number of squares in the figure is 4 + 1 + 1 = 6

Hence option C is correct.