This article provides simple tricks with formulas to find the number of triangles for the following figures
- Counting triangles within 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 the number of triangles in a square
Type – 1 : Counting triangles within Square, Rectangle, Quadrilateral
Find the number of triangles in the above figures
Figure – 1 : Number of triangles in Fig – 1 = 8
Hint: Here have a total of two diagonals and four blocks. So the formula for that 4 x 2 = 8 number of triangles.
Figure – 2 : Number of triangles in Fig – 2 = 16
Hint: Here have total two diagonals and eight blocks. So the formula for that 8 x 2 = 16 number of triangles.
Figure – 3 : Number of triangles in Fig – 3 = 18
Hint: Here each square has 8 no. of triangles and combined squares have 2 no. of triangles. So the total number of triangles – 8 + 8 + 2 = 18.
Figure – 4 : Number of triangles in Fig – 3 = 28
Hint: Here each square has 8 no. of triangles and combined squares have 4 no. of triangles. So a total number of triangles – 8 + 8 + 8 + 4 = 28.
The 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 a 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 a 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 a 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 a number of vertical parts ” 5″ and horizontal parts “3” then possible triangles is 5 x 3 x 6 /2 = 45
Type – 4 : Counting triangles within embedded Triangle
How many triangles are in the above figures
Figure – 13: Triangle counting in Fig – 13 = 5
Formula : Here number of embedded triangles in the 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 within the particular pattern of the Triangle
How many possible triangles are in the above figures
Formula to count the number of triangles like the above particular pattern type of Triangle
where “n” = number of unit triangles in a side
Note : Consider only the integer part from the answer obtained in the 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 comes 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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