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How to find number of triangles in the given figure?

Updated: Mar 30

Are you preparing for competitive exams?

So, here it is...

Each and every competitive exams will have this question. Usually, students waste time in counting the number of triangles in the given figure. It would take at least 5 to 8 mins for this question, in turn, which would affect the time limit for the entire exam.

So, here is a shortcut which can be applied to any given triangular figures. It would take 2mins maximum,in turn, saves time as TIME IS THE MOST IMPORTANT ONE TO KEEP IN MIND DURING EXAMS!!

Shortcut to calculate the number of triangles in the given figure is

n (n+2)(2n+1)/8

where

n : total number of any one side triangulat parts

Example :



There are 4 dots. So, the number of side triangles are 4 . You can consider any one side. But consider only one side.

So, n=4

Therefore,

n+1 = 4+2 = 6
2n +1 = 4*2 +1 = 9

Therefore the total number of triangles in the given figure is

n(n+1)(2n+1)/8
= 4* 6 * 9 /8
= 27

The total number of triangles in the given figure is 27


Similarly, we can apply this shortcut for all triangular based questions.

All the best for your exams!




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How final answer is 27

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