COUNTING NUMBER OF TRIANGLES IN THE GIVEN FIGURE

Count Number of Triangles in Square, Rectangle and Quadrilateral

Hint :

If the given figure has only one square or rectangle, then the formula to find the number of triangles is

Number of diagonals ⋅ Number of blocks

If it has combination of more than one squares, we have to mark the spot where it joins. In the following examples you can see it in detail.

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

Count Number of Triangles in Triangle

Hint :

To find the number of triangles in a large triangle, we should name the basements with numbers.

Then finding the total will give us the total number of triangles we have in that picture.

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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