Counting of Triangles


 
 
Concept Explanation
 

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 .

Sample Questions
(More Questions for each concept available in Login)
Question : 1

In each of the following question , find the number of triangles in the given figure .

Right Option : B
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Explanation
Question : 2

Directions : Find the number of triangles in the given figure:

Right Option : C
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Explanation
Question : 3

Directions : Find the number of triangles in the given figure

Right Option : C
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Explanation
 
 


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