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4219 3

Q: Determine the number of rectangles and hexagons in the following figure.

  • 1
    30, 5
  • 2
    32, 3
  • 3
    28, 5
  • 4
    30, 3
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Answer : 1. "30, 5"
Explanation :

Answer: A) 30, 5 Explanation: The figure may be labelled as shown     Rectangles :   The simplest rectangles are CVSR, VETS, RSWM and STKW i.e 4 in number.   The rectangles composed of two components each are CETR, VEKW, RTKM and CVWM i.e 4 in number.   The rectangles composed of three components each are ACRP, PRMO, EGHT and THIK i.e 4 in number.   The rectangles composed of four components each are CEKM, AVSP, PSWO,VGHS and SHIW i.e 5 in number.   The rectangles composed of five components each are AETP, PTKO, CGHR and RHIM i.e 4 in number.   The rectangles composed of six components each are ACMO and EGIK i.e 2 in number.   The rectangles composed of eight components each are AGHP, PHIO, AVWO and VGIW i.e 4 in number.   The rectangles composed of ten components each are AEKO and CGIM i.e 2 in number.   AGIO is the only rectangle having sixteen components   Total number of rectangles in the given figure = 4 + 4 + 4 + 5 + 4 + 2 + 4 + 2 + 1 = 30.   Hexagons :   The hexagons in the given figure are CDEKLM, CEUKMQ, CFHJMQ, BEUKNP and BFHJNP. So, there are 5 hexagons in the given figure.

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