After labelling the figure, we get the following,

• Simplest triangles IJQ, JKQ, KLQ, LMQ, MNQ, NOQ, OPQ, and PIQ (8)
• Triangles with two components each ABQ, BCQ, CDQ, DEQ, EFQ, FGQ, GHQ, HAQ, IKQ, KMQ, MOQ, and OIQ (12)
• Triangles with four components each ACQ, CEQ, EGQ, GAQ, IKM, KMO, MOI and OIK (8)
• Triangles with eight components each ACE, CEG, EGA and GAC (4)

Total number of triangles in the figure is 8 + 12 + 8 + 4 = 32

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

• Squares with two components each IJQP, JKLQ, QLMN, and PQNO (4)
• Squares with four components each ABQH, BCDQ, QDEF and HQFG (4)
• Square with eight components is IKMO (1)
• Square with sixteen components is ACEG (1)

Total number of squares in the figure is 4 + 4 + 1 + 1 = 10

Hence option C is correct.