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338                                                               Counting of Figures and Hidden Embedded Figures
                                      Answer with Explanation





                                                  Concept Applicator


            1.                    A                              3.                A


                                                                              I         H
                                                                      K                         D

                      G                             J                      J              G
                                H
                                           I
                                                                                   F

                 B                D         E              C              B                 C
                No. of Straight lines: AB, BC, CA, AD, AE, GD, GC,       Number of Triangle are ABG, AJC, EFD, DIB, AIH,
                                                                      EIJ, BJF, CFG, DGH, JFG,  IJG,  HJG,  IOH, IOJ,
                 DF = 8
                                                                      IOG, HOG.
                No. of Triangles: ABC, ABD, ADE, AEC, ABE, ADC,       Total: 19
                 AGC, BGC, BGD, DGC, GDH, HDI,  GDI,  DIE,
                 IEC, DIC, AIC, AIJ, JIC, AGI, AGH, AHI = 22          Option (d)
                Option (b)                                       4.    D          E         C

            2.               A


                                                                      G                      H
                       L           D

                    K                E


                 J                      F                             A           F          B
                                                                       Number  of triangles  are ABC,  ADC,  ADB,  BDC,
                                                                      DOC, COB,  BOA,  AOD, DOE, EOC,  AOF, FOB,
                 B     I     H     G     C
                Total Number  of triangles:                           DOG, COH, AOG, BOH.

                From the Vertex A:  ABC, AJF, AKE,  ALD               Total: 16
                From the Vertex B: BIJ, BHK, BGL                      Option (a)
                From the Vertex C: CGF, CHE, CID                 5.           H                G
                                                                          S      V   M    R
                In quad BJFC: there are 7 small triangles
                In quad KEJF:  there are 4 Small triangles            D      L   K C    N      O

                In quad KELD: there are three triangles
                                                                               E       W       F
                Total triangles 24.                                       P          J
                Option (c)                                                       I       Q


                                                                      A      U      B
                                                                      TOTAL  NUMBER OF QUADRILATERALS = 17
                                                                      Hence option (c)
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