# Thread: How many rectangles in a 10 x 10 checkerboard?

1. ## how many rectangles in a chess board

how many rectangles in a chess board, I think it is 3025 but the teacher said no

2. What was your logic that gave you that number?

3. First, I created a checkerboard on paper and wrote in each square the number of rectangles that would use that square as a bottom right corner such as this:

1 2 3 4 5 6 7 8 9 10
2 4 6 8 10 12 14 16 18 20
3 6 9 12
4 8 12 16
5 10 15 20 25
6
7
8
9
10

until I had the whole grid finished. Then I added them all up.

Also, I found an equation on the internet that is supposed find the number of rectangles in a checkerboard. (also this isncludes squares)

The formula is :

[n(n+1)/2]^2

therefore:

[10(10+1)/2]^2
=[10(11)/2]^2
=[110/2]^2
=55^2
=3025

Please, if you could help, it's really important.

4. Originally Posted by danielle_54321
First, I created a checkerboard on paper and wrote in each square the number of rectangles that would use that square as a bottom right corner such as this:

1 2 3 4 5 6 7 8 9 10
2 4 6 8 10 12 14 16 18 20
3 6 9 12
4 8 12 16
5 10 15 20 25
6
7
8
9
10

until I had the whole grid finished. Then I added them all up.

Also, I found an equation on the internet that is supposed find the number of rectangles in a checkerboard. (also this isncludes squares)

The formula is :

[n(n+1)/2]^2

therefore:

[10(10+1)/2]^2
=[10(11)/2]^2
=[110/2]^2
=55^2
=3025

Please, if you could help, it's really important.
My solution agrees with what you have found, also a Google
search seems to confirm that this is the correct answer to
the problem as stated.

Perhaps the actual wording of the problem set by your
teacher was slightly different from what you have given?

RonL

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# how many rectangle in a 10× 10 grid

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