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Determine the number of rectangles and hexagons in the given figure.

Correct Answer: 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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