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Determine the number of rectangles and hexagons in the given figure.
- a)30, 5
- b)32, 3
- c)28, 5
- d)30, 3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Determine the number of rectangles and hexagons in the given figure.a)...
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.
Most Upvoted Answer
Determine the number of rectangles and hexagons in the given figure.a)...
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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