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

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

$\frac{n \ \times m \ \times (n+1)}{2}$

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 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

$\frac{n (n+2) (2n+1)}{8}$ 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

33 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

Avika

(January 25, 2022 - 1:55 pm)

Best Website for Reasoning Preparation

sivaalluri

(February 2, 2022 - 1:12 am)

welcome

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)

Thank you Mr.Sai for your valuable comment on this article

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)

Thank for your suggestion

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 ,
your blog for these tricks is really helpful for me.
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)

Please go through the below link

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.

raj

(December 20, 2021 - 5:28 pm)

You guys are wonderful. Thanks bro

sivaalluri

(January 2, 2022 - 8:49 am)

welcome

Tony G. Parkes

(March 1, 2022 - 8:21 pm)

thanks you for such a awesome blog it is gonna to be really helpful

SHREYANSH

(May 11, 2022 - 5:18 am)

11 th question under how become 3rd horizontal

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