Diogo cut out a cross from cardboard as shown below. In this cross, all sides have a length equal to $1 \mathrm{~cm}$, and all angles are right angles. Fernanda challenged Diogo to make two straight cuts on this cross, so as to form four pieces that can be reassembled to form a square.

![](https://cdn.mathpix.com/cropped/2024_05_01_d02c2755ad3373bde08ag-03.jpg?height=481&width=479&top_left_y=603&top_left_x=860)

a) What will be the area of the square obtained?

b) What will be the side length of the square obtained?

c) Show how Diogo can make these two straight cuts so that he can form the square with the four pieces obtained from the cuts!
Solution

a) The area of the square obtained must be the same as that of the cardboard cross. Since the cardboard cross can be divided into five squares with sides equal to one, its area will be equal to $5 \mathrm{~cm}^{2}$.

b) For the area of the square obtained to be equal to $5 \mathrm{~cm}^{2}$, it is necessary that its side be equal to $\sqrt{5} \mathrm{~cm}$.

c) The two cuts that need to be made are:
![](https://cdn.mathpix.com/cropped/2024_05_01_d02c2755ad3373bde08ag-20.jpg?height=490&width=1360&top_left_y=1750&top_left_x=227)