Calculate the Area of a Shape

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Calculating the area of a shape

In this project I will investigate the area of shapes; I will investigate shapes with 3,4,5,6 and 7 dots joined and I will look at building up the dots inside the shapes.

My prediction is that shapes with the same amount of dots joined and number of dots inside, will have the same area.

After drawing the shapes I have notice that, shapes with the equal number of dots have the same area, this can be seen on the previous diagram pages. So from now on I will only draw 1 of each type of diagram.

I will now put all of my results for no dots inside into a table.

                                                  Table 1

                   

  • After creating a table 1, I have noticed a pattern in the area column.
  • The pattern is going up in ½ cm2 each time a dot is added to the edge.
  • By looking at the pattern I have created formula in both words and algebra:

Area = the number of dots   - 1          A=N – 1          

A= Area                                            2                                      2  

N= Number of dots                                          

To prove I’m right

When= N = 6           A= 6 - 1                    = 3-1

                                        2                         = 2cm2  

 

If you look at my table you will see this correct.

Now I know I am defiantly correct with my formula I can find area of a shape of any size as long as there are no dots inside.

E.G

                 N=68             A=68 – 1            = 33cm2

Now I have investigated shapes with 1 dot inside I will put my answers into a table.

 

  •  After creating a table 2, I have noticed a pattern in the area column.
  • The pattern is going up in ½ cm2 each time a dot is added to the edge.

By looking at the pattern I have created formula in both words and algebra.

Area= the number of dots         A=N

  1. 2

To show I’m right:

    When =N=6            A= 6        =3cm2

Join now!

                                           2

If you look at my table this correct.

Now I’m correct with my formula I can find area of a shape of any size as long as there is 1 dot inside.

E.G    

             N= 100       A=100          =50cm2

                                       2

Now I have investigated shapes ...

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