## Square with a hole

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 ? 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 !
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 !