COUNTING NUMBER OF TRIANGLES IN THE GIVEN FIGURE

Example 1 :

Find the number of triangles in the picture given below

Solution :

Number of diagonals  =  2

Number of blocks  =  4

So, the number of triangles to be formed  =  4 ⋅ 2

  =  8

Example 2 :

Find the number of triangles in the picture given below

Solution :

Number of diagonals  =  2

Number of blocks  =  8

So, the number of triangles to be formed  =  2 ⋅ 8

  =  16

Example 3 :

Find the number of triangles in the picture given below

Solution :

In each squares, we have two diagonals each.

Number of diagonals  =  2

Number of blocks  =  8

So, the number of triangles in the separate squares are

  =  2 ⋅ 8

  =  16

Other than this, we have two more triangles drawn above.

So, the total number of triangles =  16 + 2  ==>  18

Example 4 :

Find the number of triangles in the picture given below

Solution :

We have three squares in the given figure.

Number of diagonals in each square =  2

Number of blocks  =  8

The number of triangles in the separate squares are

  =  3 ⋅ 8

  =  24

Other than this, we have four more triangles drawn above.

So, the total number of triangles =  24 + 4  ==>  28

Example 5 :

Find the number of triangles in the picture given below

Solution :

Writing the numbers at the base, we get

So, there are 3 triangles in the picture.

Example 6 :

Find the number of triangles in the picture given below

Solution :

By writing the numbers at the base, we get

1 + 2 + 3 + 4  =  10

So, the total number of triangles we have is 10.

Example 7 :

Find the number of triangles in the picture given below

Solution :

By writing the numbers at the base, we get

Example 8 :

Find the number of triangles in the picture given below

Solution :

By writing the numbers in the base, we get

Number of rows  =  3

Sum of numbers in each row  =  1 + 2 + 3 + 4 + 5

  =  15

Number of triangles in the picture  =  3(15)

  =  45

So, the total number of triangles in the picture given above is 45.

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