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Important for :
1
find the number of triangles in the given figure.

» Explain it
D
The figure may be lebelled as shown.



The simplest triangles are AJF, FBG, GCH, HDI, and IEJ

i.e. 5 in number.

The triangles composed of three components each EBH, AIC, EFC, ADG, and BJD i.e. 5 in number.

Thus, there are 5 + 5 = 10 triangles in the figure.

Hence, option D is correct.
2
Find the number of triangles in the given figure.


» Explain it
C
The figure may be labelled as shown.
 

The simplest triangles are ABF, BFG, BCG, CGH, GHD, GED, EFG and AFE i.e. 8 in number.

The triangles composed of two components each are ABG, BGE, AGE, ABE and GCD i.e. 5 in number.

The triangles composed of three components each are BCD, CDE, BED, and BCE i.e. 4 in number.

Thus, there are 8 + 5 + 4 = 17 triangles in the figure.

Hence, option C is correct.
 

3
find the number of triangles in the given figure.


» Explain it
C
We may lebel the figure as shown.



The simplest triangles are BFG, CGH, EFM, FMG, GMN, GHN, HNI, LMK, MNK and KNJ i.e. 10 in number.

The triangles composed of three components each are FAK and HKD i.e. 2 in number.

The triangles composed of four components each are BEN, CMI, GLJ and FHK i.e. 4 in number.

The triangles composed of eight components each are BAJ and CLD i.e. 2 in number.

Thus, there are 10 + 2 + 4 + 2 = 18 triangles in the given figure.

Hence, option C is correct.
 
4
Find the number of triangles in the given figure?

» Explain it
C
We may label the figure as shown.


 
The simplest triangles are AGH, GFO, LFO, DJK, EKP, PEL and IMN i.e. 7 in number.
 
The triangles having two components each are GFL, KEL, AMO, NDP, BHN, CMJ, NEJ and HFM i.e. 8 in number.
 
The triangles having three components each are IOE, IFP, BIF and CEI i.e. 4 in number.
 
The triangles having four components each are ANE and DMF i.e. 2 in number. 
 
The triangles having five components each are FCK, BGE and ADL i.e. 3 in number. 
 
The triangles having Six components each are BPF, COE, DHF and AJE i.e. 4 in number. 

Thus, there are 7 + 8 + 4 + 2 + 3 + 4 = 28 triangles in the figure. 
 

5
Find the number of triangles in the given figure.

» Explain it
A
The figure may be labelled as shown.



The simplest triangles are GLK, DLJ, DJM, HMN, QRE, IRA, IPA and FPO i.e. 8 in number. 
 
The triangle having two components each are BDO, CDQ, DLM, PRA, KFI, NEI, HJI, GJI, DKI and DNI i.e. 10 in number.
 
The triangles having four components each are DIE, DFI, DOA, DQA and GHI i.e. 5 in number.
 
The triangles having six components each are DCA and DBA i.e. 2 in number.
 
DEF is the only triangle having eight components.
 
ABC is the only triangle having twelve components.
 
Thus, there are 8 + 10 + 5 + 2 + 1 + 1 =27 triangles in the figure. 

Hence, option A is correct.