After labelling the figure, we get the following,

• Simplest triangles BPN, PNE, ABM, EFG, MLK, GHI, QRO, RSO, STO and QTO (10)
• Triangles with two components each BPE, TQR, QRS, RST, and STQ (5)
• Triangles with three components each MPO and GPO (2)
• Triangles with six components each LPJ, HPJ, and MPG (3)
• Triangle with twelve components is LPH (1)

Total number of triangles in the figure is 10 + 5 + 2+ 3 + 1 = 21

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

• Squares with two components each KJOM and JIGO (2)
• Squares with four components each ANOM, NFGO and CDEB (3)
• Square composed of four components is QRST (1)
• Square composed of ten components is AFIK (1)

Total number of squares in the figure is 2 + 3 + 1 + 1 = 7

Hence option A is correct.