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Investigation to find out a formula for rectangles on different grid sizes.

Extracts from this document...

Introduction

Mariela Mezquita 10ª

Math, Mr Bhoja

30 April 2008

COURSEWORK

Aim: To find out a formula for rectangles on different grid sizes.

That is done by multiplying the corners of the rectangle and then we subtract them.

Hypothesis:

Eg. (on a 10x10 grid size with a 2x3 rectangle)

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3 x 11= 33

1 x 13=13

33-13 = 20

Then, move on the rectangle.

A 2 x 3 cube…

image00.png

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image10.png

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As we can see, when we have a 2 x 3 rectangle, the final result will always be 20.

Explanation:

If we substitute the

...read more.

Middle

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It will always be 60..

Explanation:

x

x+3

x+20

x+23

 x(x+23)

 x+3(x+20)

expand

x(x+23) = x²+23x

 x+3(x+20) = x²+20x+3x+60

x²+23ximage02.pngimage02.png

x²+20x+3x+60

                 =60image03.png

x² and 23x cancel each other out, leaving us with a result of 60.

image04.png

If we change the

...read more.

Conclusion

3 X 4 RECTANGLE ON ANY GRID SIZE

image17.png

So:

3x4 = 6n        

FORMULA ABOVE ONLY APLLIES FOR A 4 X 5 RECTANGLE ON ANY GRID SIZE

image18.png

So:

4x5= 12n

FORMULA ABOVE ONLY APLLIES FOR A 5 X 6 RECTANGLE ON ANY GRID SIZE

image19.png

So:

5x6= 20n

FORMULA ABOVE ONLY APLLIES FOR A 6 X 7 RECTANGLE ON ANY GRID SIZE

image20.png

So:

6x7= 30n

Overall Formula:

N(H-1)(L-1)

image05.png

image07.pngimage06.png

image21.png

image22.png

Extension:

In my extension I will draw crosses instead of rectangles. Multiply the opposite sizes and try to find out a formula.

Hypothesis: I think it will be similar to the rectangle formula but a little bit more complicated.

Example:

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image08.pngimage09.png

...read more.

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