Find the number of triangles in the given figure.
A.
28
B.
32
C.
36
D.
40
Correct answer is C
The figure may be labelled as shown.
The simplest triangles are AML, LRK, KWD, DWJ, JXI, IYC, CYH, HTG, GOB, BOF, FNE and EMA i.e. 12 in number.
The triangles composed of two components each are AEL, KDJ, HIC and FBG i.e. 4 in number.
The triangles composed of three components each are APF, EQB, BQH, GVC, CVJ, IUD, DUL and KPA i.e. 8 in number.
The triangles composed of six components each are ASB, BSC, CSD, DSA, AKF, EBH, CGJ and IDL i.e. 8 in number.
The triangles composed of twelve components each are ADB, ABC, BCD and CDA i.e. 4 in number.
Total number of triangles in the figure = 12 + 4 + 8 + 8 + 4 = 36.