Counting of Triangles
Counting of Triangles
Counting of Triangles
Example : Find the number of triangles in the given figure
A. 11
B. 13
C. 15
D. 17
Answer : C
Explanation : We may label the figure as shown .
The simplest triangle are AFB`, FEB, EBC, DEC, DFE and AFD i.e. 6 in number . The triangles composed of two components each are AEB, FBC, DFC, ADE, DBE and ABD i.e. 6 in number . The triangles composed of three components each are ADC and ABC i.e. 2 in number . There is only one triangles i.e. DBC which is composed of four components . Thus , there are 6+6+2+1 = 15 triangles in the figure .
Example : Find the number of triangles in the given figure:
A. 16
B. 22
C. 28
D. 32
Answer : C
Explanation : We shall label the figure as shown :
The simplest triangles are AFJ ,FJK , FKB, BKG, JKG, JGC, HJC, HIJ, DIH, DEI, EIJ, and AEJ i.e. 12 in number . The number composed of two components each are JFB , FBG, BJG, JFG, DEJ, EJH, DJH and DEH i.e. 8 in number . The triangles composed of three components each are AJB, JBC, DJC and ADJ i.e. 4 in number . The triangles composed of six components each are DAB, ABC, BCD, and ADC i.e. 4 in number. Thus , there are 12+8+4+4 = 28 triangles in the figure .
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| Right Option : C | |||||
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| Right Option : C | |||||
| View Explanation | |||||
Directions : Find the number of triangles in the given figure:
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| Right Option : C | |||
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