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Solutions

Single component Triangle AMB, AMH, MGH, BMG, GNI, GNH, HNJ, NIJ, IOJ, JOL, KOL, IOK, KPD, DPE, LPE, LPK, BCD and AFE =18
Two Component - ABH, BHG, ABG, AGH, GIH, IHJ, GHJ , GIJ , IJK, JKL , IJL , IKL, KDE, KLE, KDL, LDE= 16
Four component triangle BHI, AGJ, GJK, HIL, ILD, JKE = 6
Total= 18 +16 +6 =40