Instructions

We cut the square A in 4 similar shapes. To do that have made two perpendiculars cuts that goes both through the center.

Then we take the pieces to make B shape.

What's the area of the B square if the original square have a side of 16 and the smallest side of each piece has a length of 2 ?

Then we take the pieces to make B shape.

What's the area of the B square if the original square have a side of 16 and the smallest side of each piece has a length of 2 ?

Dumy solution

We will calculate the length of the side of B.

The length is equal to the length of the cut in the square A

It can be computed with help of this diagram :
[display]|AC|=\sqrt{|BC|^2+|AB|^2}[/display]
[display]|BC|=8[/display]
[display]|AB|=8-5[/display]
Small shortcut : 3,4,5 is the Pythagora triplet so |AC|=5

The B square is 400 cm² !

The length is equal to the length of the cut in the square A

It can be computed with help of this diagram :

The B square is 400 cm² !

Smart solution (click to open)

The area of the square is the area of the square A to wich you add the area of the square hole

The side of the square hole is : [display][\text{Side of A}]-2\times [\text{smallest side of a piece]}[/display] [display]16-2\times 2=12[/display] So, the area is given by: [display]16^2+12^2=400[/display] The B square is 400 cm² !

The side of the square hole is : [display][\text{Side of A}]-2\times [\text{smallest side of a piece]}[/display] [display]16-2\times 2=12[/display] So, the area is given by: [display]16^2+12^2=400[/display] The B square is 400 cm² !