An exploration of tilted squares

Topic:
Square
An exploration of tilted squares which leads to the discovery of a famous theorem.
1) Is it possible to arrange the blue shapes such that they fit inside the yellow square? 2) Is it possible to arrange the red shapes such that they fit inside the other yellow square? 3) What do you notice about the area of the yellow squares? 4) What is the area of each of the blue pieces? 5) What is the area of each of the red pieces? 6) As a result of your findings in 3), what can you say about the total area of the blue pieces and the total area of the red pieces? 7) What is the area of the tilted square?