• ( 1 ) How many triangles are there in the given figures?

    • 1) 9
    • 2) 10
    • 3) 11
    • 4) 12
    • Discussion in forum
      Answer : 4) 12
      Solution : The figure may be labelled as shown.

      Name of Triangles are:
      ADE, AEF, BDE, BCE, CEF, ADC, ACE, ABC
      Thus, there are 12 triangles in the given figure.








      discussion


      Answer : 4) 12

    • ( 2 ) How many squares are there in the given figures?

    • 1) 8
    • 2) 7
    • 3) 6
    • 4) 9
    • Discussion in forum
      Answer : 3) 6
      Solution : The figure labelled as shown.

      The squares composed of two components each are BKOJ, KDFO, OFGH and JOHI i.e. 4 in number.
      There is only one square i.e. CDOB composed of four components.
      There is only one square i.e. BDGI composed of eight components.
      Thus, there are 4 + 1 + 1 = 6 squares in the given figure.








      discussion


      Answer : 3) 6

    • ( 3 ) How many triangles are there in the given figures?

    • 1) 23
    • 2) 22
    • 3) 21
    • 4) 18
    • Discussion in forum
      Answer : 4) 18
      Solution : The figure labelled as shown.

      The simplest triangles are BFG, CGH, EFM, FMG, GMN, GHN, HNI, LMK, MNK and KNJ i.e. 10 in number.
      The triangles composed of three components each are FAK and HKD i.e. 2 in number.
      The triangles composed of four components each are BEN, CMI, GLJ and FHK i.e. 4 in number.
      The triangles composed of eight components each are BAJ and CLD i.e. 2 in number.
      Thus, there are 10 + 2 + 4 + 2 = 18 triangles in the given figure.








      discussion


      Answer : 4) 18

    • ( 4 ) How many squares are there in the given figures?

    • 1) 21
    • 2) 25
    • 3) 26
    • 4) 27
    • Discussion in forum
      Answer : 1) 21
      Solution : The figure labelled as shown.

      Big square = ADHE
      Small squares = 12
      Other squares = ACOM, BDPN, MOGE, NPHF, JLTR, IKSQ, ADTQ, EHLI.
      Total squares = 1 + 12 + 8 = 21.








      discussion


      Answer : 1) 21

    • ( 5 ) How many rectangles are there in the gioven figures?

    • 1) 8
    • 2) 9
    • 3) 10
    • 4) 11
    • Discussion in forum
      Answer : 2) 9
      Solution : The figure labelled as shown.

      The simplest rectangles are ABJI, BCKJ, IJFG and JKEF i.e. 4 in number.
      The rectangles composed of two components each are ACKI, BCEF, IKEG and ABFG i.e. 4 in number.
      The only rectangle composed of four components is ACEG.
      Thus, there are 4 + 4 + 1 = 9 rectangles in the given figure.








      discussion


      Answer : 2) 9

    • ( 6 ) How many triangles are there in the given figures?

    • 1) 20
    • 2) 28
    • 3) 26
    • 4) 29
    • Discussion in forum
      Answer : 2) 28
      Solution : The figure labelled as shown.

      The simplest triangles are JBO, BKO, KDO, DFO, FGO, GHO, HIO, IJO, ABJ, BCK, CKD and DEF i.e.12 in number.
      The triangles composed of two components each are IBO, BDO, DGO, GIO, ABO, CDO, CBO, CBD and DEO i.e. 9 in number.
      The triangles composed of four components each are IBD, BDG, DGI, GIB, ACO and COE i.e. 6 in number.
      There is only one. triangle i.e. ACE composed of eight components.
      Thus, there are 12 + 9 + 6 + 1 = 28 triangles in the given figure.








      discussion


      Answer : 2) 28

    • ( 7 ) How many squares are there in the given figures?

    • 1) 20
    • 2) 21
    • 3) 27
    • 4) 25
    • Discussion in forum
      Answer : 3) 27
      Solution : The figure labelled as shown.

      The simplest squares are EFRQ, MQYX, QRZY, RNSZ, LXWK, XYA1W, YZB1A1, ZSTB1, SGHT, WA1VP, A1B1UV, B1TOU and VUIJ i.e. 13 in number.
      The squares having two components each are AEYL, FBGZ, KA1JD and B1HCI i.e. 4 in number.
      The squares having four components each are MRB1W, QNTA1, XZUP and YSOV i.e. 4 in number.
      The squares having seven components each are AFB1K, EBHA1, LZID and YGCJ i.e. 4 in number.
      There is only one square i.e. MNOP composed of nine components.
      There is only one square i.e. ABCD composed of seventeen components.
      ∴ There are 13 + 4 + 4 + 4 + 1 + 1 = 27 squares in the figure.








      discussion


      Answer : 3) 27

    • ( 8 ) How many rectangles are there in the given figures?

    • 1) 22
    • 2) 20
    • 3) 16
    • 4) 15
    • Discussion in forum
      Answer : 2) 20
      Solution : The figure labelled as shown.

      The rectangles composed of two components each are HIJE, EKJ,F, FMNG, GPQH, AEOH, EBFO, OFCG and HOGD i.e. 8 in number.
      The rectangles composed of four components each are ABFH, BCGE, CDHF, DAEG and EFGH i.e. 5 in number.
      The rectangles composed of six components each are IJFG, KLGH, MNHE and PQEF i.e. 4 in number.
      The rectangles composed of eight components each are IJMN, KLPQ and ABCD i.e. 3 in number.
      Thus, there are 8 + 5 + 4 + 3 = 20 rectangles in the given figure.
      (Here note that the squares are also counted amongst rectangles)








      discussion


      Answer : 2) 20

    • ( 9 ) How many rectangles are there in the given figures?

    • 1) 6
    • 2) 4
    • 3) 8
    • 4) 10
    • Discussion in forum
      Answer : 3) 8
      Solution : The figure labelled as shown.

      Name of rectangles are:
      ABFE, CDEF, AGHD, BCHG, IOPK, OJLP, IMNJ, LNMK.
      Thus, there are 8 rectangles in the given figure.








      discussion


      Answer : 3) 8

    • ( 10 ) How many squares are there in the given figures?

    • 1) 16
    • 2) 18
    • 3) 20 or more
    • 4) 19
    • Discussion in forum
      Answer : 3) 20 or more
      Solution : The figure labelled as shown.

      Name of squares are:
      Big square: ABCD
      Small squares : 16
      Other squares ; AFRP, FRTB, RTCI, RIDP, LNXV
      Thus, there are 22 squares in the given figure.








      discussion


      Answer : 3) 20 or more





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