Count the number of triangles and squares in the given figure.

Options

A. 44 triangles, 10 squares
B. 42 triangles, 10 squares
C. .27 triangles, 6 squares
D. 36 triangles, 9 squares

Answer

A

Explanation

The figure may be labelled as shown.

The simplest triangles are AEI, EOI, OHQ HAI, EBJ, BFJ. FOJ, OEJ, HOL, OGL, GDL, DHL, OFK, FCK, CGK and GOK i.e. 16 in number
The triangles composed of two components each are HAE, AEO, EOH, OHA, DEB, EBF, BFO, FOE, DHO, HOG, OGD, GDH, GOREOFO, FCG and CGO i.e. 16 in number.
The triangles composed of four components each are HEF, EFG, FGH, GHE, ABO, BGO, CDO and DAO i.e. 8 in number
The triangles composed feich components each are DAB, ABC, BCD and CDA i.e. 4 in number.
Total number of triangles in the figure = 16+16 +8+4 = 44.
Squares:
The The squares composed by two components are HIOL, IEJO, JFKO and KGLO i.e. 4 in number,
The squares composed of four components are AEOH, EBFO, OFGC and HOGD i.e.4 in number.
Therods only unexquare EFGH which is composed of eight components.
There is only ghe square ABCD which is composed of sixteen components.
Total number of squares in the figure = 4 +4+1+1 = 10.