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

Options

A. 26 triangles, 5 squares
B. 28 triangles, 5 squares
C. 26 triangles, 6 squares
D. 28 triangles, 6 squares

Answer

D

Explanation

The figure may be labelled as shown.

The simplest triangles are JBO, BKO, KDO, DFO, FGO, GHO. HIQ, 1JQ, ABJ, BCK, CKD and DEF 1.e.12 in number.
The triangles composed of two components each are IBO, BDO, DGO, GIO, ABO, CDO, CBO, CBD and DEO i.e. 9 in number.
The triangles composed of four components each are IBD BDG, DGI, GIB, ACO and COE i.e. 6 in number.
There is only one triangle i.e. ACE composed theight components.
Thus, there are 12+9+6+1 = 28 triangles
Thus given figure, Squares: The squares composed of two components each ate BKOJ, KDFO, OFGH and JOHI i.e. 4 in number.
There is only one square i.e. CDOB composed of four components.
There is only one square i.e. BDCI composed of eight components.
Thus, there are 4 + 1 + 1 = squares in the given figure.