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, DO EGO, GHO, HIO, IJO, ABJ, BCK, CKD and DEF i.e. 12 in number.
The triangles composed of two components excipere IBO, BDO, DGO, GIO, ABO, CDO, CBO, CBD and DEO i.e. 9 in number.
The triangles composed of four compononts each are IBD, BDG, DGI, GIB, ACO and COE i.e. 6 in number.
There is only one triangle i.e. ACE composed of eight components.
Thus, there are 12 +9+6+1= 28 triangles in the given figure.
Squares:
The squares composed of two components each are 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. BDGI composed of eight components.
Thus, there are 4 + 1 + 1 = 6 squares in the given figure,