Find the number of triangles in the given figure.
A.
16
B.
18
C.
19
D.
21
Correct answer is D
The figure may be labelled as shown.
The simplest triangles are EFH, BIC, GHJ, GIJ, EKD and CKD i.e. 6 in number.
The triangles composed of two components each are ABJ, AFJ, GCK, GEK, CED arid GHI i.e. 6 in number.
The triangles composed of three components each are GCD, GED, DJB and DJF i.e. 4 in number.
The triangles composed of four components each are ABF and GCE i.e. 2 in number.
The triangles composed of five components each are ABD and AFD i.e. 2 in number.
There is only one triangle i.e. FBD composed of six components.
Total number of triangles in the figure = 6 + 6 + 4 + 2 + 2 + 1 = 21.
