# Tricks to find the number of triangles in the given figure

31 August 2023

31 August 2023

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While solving various Entrance tests, you may come across questions regarding calculation of number of various geometrical figures, lets learn some shortcuts and tricks to calculate the number of such geometrical figures in fraction of seconds.

Here we will learn tips and Shortcut to find the number of triangles in the given figure-

One shortcut for calculating the number of triangles that can be formed using a given number of points is to use the formula n*(n-1)*(n-2)/6. This formula works by taking the total number of points (n), subtracting 1 to account for the first point, subtracting another 1 to account for the second point, and then dividing by 6 to account for the fact that each triangle can be formed in 3 different ways (by choosing different combinations of 3 points).

For example, if you have 10 points, you can use the formula to calculate the number of triangles as follows:

n = 10

n-1 = 10-1 = 9

n-2 = 9-1 = 8

n*(n-1)(n-2)/6 = 109*8/6 = 120/6 = 20

Therefore, there are 20 different triangles that can be formed using 10 points.

This shortcut can be useful for quickly calculating the number of triangles that can be formed using a large number of points, without having to consider all the different combinations of 3 points. However, it is important to keep in mind that this formula only works for calculating the number of triangles that can be formed using non-collinear points (i.e. points that do not lie on a straight line).