Question

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

• A. 30, 5
• B. 32, 3
• C. 28, 5
• D. 30, 3

Answer 1

The correct option is A 30, 5

Rectangle:
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.
The figure may be labelled as shown.