Count the Number of Triangles in the Given Figure Formula

Counting of Triangles in the Figure

Dear Students, in this post we are sharing Shortcuts to Count Number of Triangles in the given geometrical figure. Its very important topic of non-verbal reasoning subject. Mostly 1 or 2 questions always ask in the SSC(CGL, CHSL, MTS, CPO & Others), Railway(RRB NTPC, RPF, Group D, ALP, TC & Others) and other government examinations. Many candidates confused to count Number of Triangles. After reading this post, they must will count the correct number of triangles, we hope!.

How Many Triangles are there in the Given Figure?
>>Figure Type1: Triangle having number of bisects with vertex
>>Figure Type2: Square, Rectangle and Quadrilateral
>>Figure Type3: Particular Pattern of Triangle
>>Figure Type4: Embedded Triangle having number of bisects with vertex
>>Figure Type5: Triangle having number of bisects with vertex and Horizontal Lines

>>Figure Type1: Triangle having number of bisects with vertex
Q1.How Many Triangles are there in the Given Figure?

Ans & Solution-
[Shortcut-Count the number of blocks made by bisects with vertex and add the number to know total number of triangles in this type of figures]

Number of triangles=1+2=3

Q2.How Many Triangles are there in the Given Figure?

Ans & Solution-
[Shortcut-Count the number of blocks made by bisects with vertex and add the number to know total number of triangles in this type of figures]

Number of triangles=1+2+3=6

Q3.How Many Triangles are there in the Given Figure?

Ans & Solution-
[Shortcut-Count the number of blocks made by bisects with vertex and add the number to know total number of triangles in this type of figures]

Number of triangles=1+2+3+4=10

>>Figure Type2: Square, Rectangle and Quadrilateral
Q4.How Many Triangles are there in the Given Figure?

Ans & Solution-
[Shortcut-Count the number of blocks and multiply it with number of diagonals drawn to know total number of triangles in this type of figures]

Number of triangles=4*2=8

Q5.How Many Triangles are there in the Given Figure?

Ans & Solution-
[Shortcut-Count the number of blocks and multiply it with number of diagonals drawn to know total number of triangles in this type of figures]

Number of triangles=8*2=16

Q6.How Many Triangles are there in the Given Figure?

Ans & Solution-
[Shortcut-do separate operation of each square first of Counting the number of blocks and multiply it with number of diagonals drawn and then combine both square and then see the triangle developed in shaded region and then add all]

Number of triangles=4*2 + 4*2 + 2= 8+8+2=18

Q7.How Many Triangles are there in the Given Figure?

Number of triangles=4*2+4*2+4*2+2+2=8+8+8+4=28

>>Figure Type3: Particular Pattern of Triangle
Q8.How Many Triangles are there in the Given Figure?

Ans & Solution-
[Shortcut-Count the number of blocks made by vertical line(x) and number of blocks made by horizontal line(y) and apply the formula given below to know total number of triangles in this type of figures]
Number of triangles=[x*y(x+1)]/2

Number of blocks made by vertical line(x)=1=ABC
and Number of blocks made by horizontal line(y)=2=BCED and ADE
Therefore,
Number of triangles=[1*2(1+1)]/2
=[2(2)]/2
=[4]/2
=2
See & Throw Solution- Number of triangles=2=ABC and ADE

Q9.How Many Triangles are there in the Given Figure?

Number of blocks made by vertical line(x)=2=ABF and AFC
and Number of blocks made by horizontal line(y)=2=BCED and ADE
Therefore,
Number of triangles=[x*y(x+1)]/2
=[2*2(2+1)]/2
=[4(3)]/2
=12/2
=6

Q10.How Many Triangles are there in the Given Figure?

Number of blocks made by vertical line(x)=4=ABC,ACD,ADE and AEF
and Number of blocks made by horizontal line(y)=3=HBFJ, GHJI and AGI
Therefore,
Number of triangles=[x*y(x+1)]/2
=[4*3(4+1)]/2
=[12(5)]/2
=60/2
=30

Q11.How Many Triangles are there in the Given Figure?

Number of blocks made by vertical line(x)=5=ABC, ACD, ADE, AEF and AFG
and Number of blocks made by horizontal line(y)=3=IBGK,HIKJ and AHJ
Therefore,
Number of triangles=[x*y(x+1)]/2
=[5*3(5+1)]/2
=[15(6)]/2
=90/2
=45

>>Figure Type4: Embedded Triangle having number of bisects with vertex
Q12.How Many Triangles are there in the Given Figure?

Ans & Solution-
[Shortcut-Count the number of triangles embedded inside of the triangle and count horizontal blocks and put it in the formula given below to know total number of triangles in this type of figures]
Number of triangles=4n+m
where n= number of triangles embedded inside of the triangle
and m= number of horizontal blocks
In the figure below,

Number of triangles embedded inside of the triangle, n = 1(ECF)
Number of horizontal blocks, m=1(BDFE)
Number of triangles=4n+m
=4*1+1
=4+1
=5

Q13.How Many Triangles are there in the Given Figure?

Number of triangles embedded inside of the triangle, n = 2(BEC and GHI)
Number of horizontal blocks, m=1(BDFC)
Number of triangles=4n+m
=4*2+1
=8+1
=9

Q14.How Many Triangles are there in the Given Figure?

Number of triangles embedded inside of the triangle, n = 3(ECF, GHI and JLK)
Number of horizontal blocks, m=1(BDFE)
Number of triangles=4n+m
=4*3+1
=12+1
=13

>>Figure Type5: Triangle having number of bisects with vertex and Horizontal Lines
Q15.How Many Triangles are there in the Given Figure?

Ans & Solution-
[Shortcut-Count the number of unit triagnles in a side and put it in the formula given below to know total number of triangles in this type of figures]
Number of triangles=[x(x+2)(2x+1)]/8
[Note- Take integer part only if you get decimal digits in the operation.]
In the figure below,

Number of unit triagnles in a side=3
Number of triangles=[x(x+2)(2x+1)]/8
=[3(3+2)(2*3+1)]/8
=[3*5(6+1)]/8
=[3*5*7]/8
=105/8
=13.125=13

Q16.How Many Triangles are there in the Given Figure?

Number of unit triagnles in a side=4
Number of triangles=[x(x+2)(2x+1)]/8
=[4(4+2)(2*4+1)]/8
=[4(6)(8+1)]/8
=[4*6*9]/8
=216/8
=27

Q17.How Many Triangles are there in the Given Figure?

Number of unit triagnles in a side=13
Number of triangles=[x(x+2)(2x+1)]/8
=[13(13+2)(2*13+1)]/8
=[13(15)(26+1)]/8
=[13*15*27]/8
=5265/8
=658.125=658

Answer the following Questions made for you, write your answer in the comment box-
Q1. How Many Triangles are there in the Given Figure?