# 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 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 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 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 Count the number of triangles in the above  picture

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

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

Formula : Here number of vertical parts ” n” and horizontal parts “m” then possible triangles  is 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 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 How many possible triangles are in the above figures

Formula to count number of triangles like above particular pattern type of Triangle 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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## 25 thoughts on “Find the Number of triangles in the given figure | Count the number of triangles” (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) #### Suresh

(January 4, 2019 - 5:19 pm)

Super #### sivaalluri

(January 27, 2019 - 4:10 am)

Thank you #### Om Namah Sivay allurian

(February 7, 2019 - 4:12 am)

Thanks a lot for the tricks.
They are used in all competitive exams. #### sivaalluri

(February 20, 2019 - 3:26 pm)

Thank you #### sai manne

(March 26, 2019 - 7:13 am)

This is the best website to learn to count no. of triangles lesson. Because most of the websites I’ve seen are showing wrong and different answers for the same question. Finally, I am here happy to find valid and correct answers, and also methods to do it in the right way. Thanx a lot. #### sivaalluri

(April 6, 2019 - 2:38 pm) #### S. Chidambaranathan

(April 7, 2019 - 12:49 am)

Really loved it. I really wanted this. But please make your website secure #### sivaalluri

(April 20, 2019 - 3:14 pm) #### Sagarika

(October 23, 2019 - 3:37 pm)

Thanks lot #### sivaalluri

(October 27, 2019 - 3:34 am)

welcome sagarika #### devendra

(May 3, 2019 - 8:17 pm)

hello sir ,
i just want to how we can find no .of triangles in triangle when it has three medians intersect each other #### sivaalluri

(May 10, 2019 - 3:43 pm)

Number of triangles in a figure telugu | number of triangles in a triangle in telugu | Count triangles in telugu
https://youtu.be/2RPCPQC24k4 #### devendra

(May 3, 2019 - 8:26 pm)

sir ,
it seems that Type -3 formula fails in case if horizantal and vertical lines are same in a triangle #### sivaalluri

(May 10, 2019 - 3:47 pm)

no it works well #### shyam

(June 2, 2019 - 6:04 pm)

bro for this your assumption and tricks are good to solve but what to do when all the above are jumbled to single diagram ……or some another diagram (example is civils prelims triangle sum ) #### sivaalluri

(June 4, 2019 - 2:46 pm)

Ok we will correct it #### Hitler

(December 27, 2019 - 8:30 am)

Thanks #### sivaalluri

(December 29, 2019 - 1:59 pm)

Welcome #### Aayush

(January 18, 2021 - 3:44 pm)

Very nice and helpful tricks. Can you please add their derivations also? I have derived some of them using combinatorics. Need help in derivations of others. #### MOIN KHAN

(April 24, 2020 - 1:52 am)

Bhai Mza aa gay……. #### sivaalluri

(April 26, 2020 - 11:23 am)

Welcome #### Chukwuma

(September 16, 2021 - 8:37 pm)

Thanks so much, I have learnt alot from you guys. #### sivaalluri

(September 18, 2021 - 5:33 am)

welcome