Count the number of triangles and squares in the given figure.
21 triangles, 7 squares
18 triangles, 8 squares
20 triangles, 8 squares
22 triangles, 7 squares
Correct answer is A
The figure may be labelled as shown.
Triangles :
The simplest triangles are BPN, PNE, ABM, EFG, MLK, GHI, QRO, RSO, STO and QTO i.e. 10 in number.
The triangles composed of two components each are BPE, TQR, QRS, RST and STQ i.e. 5 in number.
The triangles composed of three components each are MPO and GPO i.e. 2 in number.
The triangles composed of six components each are LPJ, HPJ and MPG i.e. 3 in number.
There is only one triangle LPH composed of twelve components.
Total number of triangles in the figure = 10 + 5 - 2 + 3 + 1 = 21.
Squares :
The squares composed of two components each are KJOM and JIGQ i.e. 2 in number.
The squares composed of three components each are ANOM, NFGO and CDEB i.e.3 in number.
There is only one square i.e. QRST composed of four components.
There is only one square i.e. AFIK composed of ten components.
Total number of squares in the figure = 2 + 3 + 1 + 1 = 7.
