Find the Number of triangles in the given figure | Count the number of triangles

In this article provides the simple tricks with formulas to find the number of triangles for the following figures

  • Counting triangles with in Square, Rectangle, Quadrilateral 
  • Number of possible triangles within a triangle

how many number of triangles | counting figures in reasoning tricks

How to Calculate Number of Triangles in a Square | Trick to Count no of Triangles

Calculate number of triangles in a square

Type – 1 : Counting triangles with in Square, Rectangle, Quadrilateral 

Find the Number of triangles | Calculate number of triangles in a square | allmathtricks

Find the number of triangles in the above figures

Figure – 1 : Number of triangles in Fig – 1 =  8

Hint: Here having total  two diagonals and having four blocks. So formula for that 4 x 2 = 8 number of triangles.

Figure – 2 : Number of triangles in Fig – 2  =  16

Hint: Here having total  two diagonals and having eight blocks. So formula for that 8 x 2 = 16 number of triangles.

Figure – 3 : Number of triangles in Fig – 3  =  18

Hint: Here each square having 8 no. of triangles and combine squares having 2 no. of triangles. So total number of   triangles – 8 + 8 + 2 = 18.

Figure – 4 : Number of triangles in Fig – 3  =  28

Hint: Here each square having 8 no. of triangles and combine squares having 4 no. of triangles. So total number of   triangles – 8 + 8 + 8 + 4 = 28.

Trick to count no of triangles : Intersection of diagonals in a square, rectangle, rhombus, parallelogram, quadrilateral and trapezium will give eight triangles.

Type – 2 : Counting triangles with the Triangle having number of bisects with vertex

how many number of triangles | trick to count no of triangles

Count the number of possible triangles in the above figures

Figure – 5: Number of possible triangles in Fig – 5 =  1

Figure – 6 : Number of possible triangles in Fig – 6 =  3

Formula : Here number of parts ” n”  then possible triangles  is n (n+1) /2

Figure – 7 : Number of possible triangles in Fig – 7 =  10

Hint : No of parts ” n” = 4 so according to formula 4 x 5 /2 = 10

Figure – 8 : Number of possible triangles in Fig – 8 =  15

Hint : No of parts ” n” = 5 so according to formula 5 x 6 /2 = 15.

Type – 3 : Counting triangles with the Triangle having number of bisects with vertex and horizontal lines

how many triangles puzzle formula | number of triangles

 

Count the number of triangles in the above  picture

Figure – 9: Triangle counting in Fig – 9 =  2

Figure – 10: Triangle counting in Fig – 9 =  6

Formula : Here number of vertical parts ” n” and horizontal parts “m” then possible triangles  is nm (n+1) /2

Figure – 11: Triangle counting in Fig – 11 =  30

Solution : Here number of vertical parts ” 4″ and horizontal parts “3” then possible triangles  is 4 x 3 x 5 /2 = 30

Figure – 12: Triangle counting in Fig – 12 =  45

Solution : Here number of vertical parts ” 5″ and horizontal parts “3” then possible triangles  is 5 x 3 x 6 /2 = 45

Type – 4 : Counting triangles with in embedded Triangle

 how many rectangles are there in the given figure | number of triangles points

How many triangles are in the above figures

Figure – 13: Triangle counting in Fig – 13 =  5

Formula : Here number embedded triangles in outer triangle ” n” and horizontal parts “m” then possible triangles  is 4n + 1

Figure – 14: Triangle counting in Fig – 14 =  9 ( Here n= 2 )

Figure – 15: Triangle counting in Fig – 15 =  13 ( Here n= 3 )

Type – 4 : Counting triangles with in the  particular pattern of Triangle

number of triangles with given parts | Find the number of triangles in the given figure

How many possible triangles are in the above figures

Formula to count number of triangles like above particular pattern type of Triangle

\frac{n (n+2) (2n+1)}{8}   where  “n”  = number of unit triangles in a side

Note : Consider only integer part from answer obtained in above formula ( For example the answer may come 13.12 then consider only “13”. Also remember You don’t have to round off the number for example answer may come 36.8 then consider only “36”.

Figure – 16: No of triangles in Fig – 16 =  13 ( Here n= 3 )

Solution: According to above formula 3 x 5 x 7 /8 = 13.12 so consider integer only i.e 13

Figure – 17: No of triangles in Fig – 17 =  27 ( Here n= 4 )

Solution: According to above formula 4 x 6 x  9/8 = 27

Figure – 18: No of triangles in Fig – 18 =  170 ( Here n= 8 )

Solution: According to above formula 8 x 10 x  17/8 = 170

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Post Author: sivaalluri

My self Sivaramakrishna Alluri. Thank you for watching my blog friend

2 thoughts on “Find the Number of triangles in the given figure | Count the number of triangles

    Shashi Totad

    (November 17, 2018 - 4:53 am)

    U people r just awesome… I was literally struggling to solve these problems in my police sub-inspector exams… But now I just spent 30 min …Ready to solve complex problems..Thanks a ton for ur genuine efforts…way to go keep up the same work going on.

    Regards,
    Shashi

      sivaalluri

      (November 18, 2018 - 2:04 pm)

      Thank you Mr.Shashi Totad for your valuable comments

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