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 – 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 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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## 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