After labelling the figure, we get the following,

• Simplest triangles ABL, BCD, DEF, FGP, PGH, QHI, JQI, KRJ and LRK (9)
• Triangles with two components each OSG, SGO, SPI, SRI, HSQ, KMS, FGH, JHI and JKL (9)
• Triangle with four components is KSG (1)
• Triangles with five components each NEI, ANI, MCG and KCO (4)
• Triangles with six components each GMK and KOG (2)
• Triangle with ten components is AEI (1)
• Triangle with eleven components is KCG (1)

Total number of triangles in the figure is 9 + 9 + 1+ 4 + 2 + 1 + 1=27

Hence option D is correct.