6) The four squares in the drawing have the same side. In what ratio do the areas of the three shaded figures stand?
![](https://cdn.mathpix.com/cropped/2024_04_17_58bef2a2a14f9f84b61bg-1.jpg?height=270&width=946&top_left_y=506&top_left_x=1663)

(A) The first area is greater than the other two

(B) the second area is greater than the other two

(C) the third area is greater than the other two

(D) the first area is equal to the second, and both are greater than the third

(E) the three areas are equal.
6) The answer is $\mathbf{( E )}$.

Assuming the side of the squares measures 2, it is immediately obtained that:

- the area of the first figure is $2 \cdot \frac{1}{2}=1$,
- the area of the second figure is 1,
- the area of the third figure is $2 \cdot\left(\frac{\sqrt{2}}{2}\right)^{2}=1$.

Second SOLUTION

The answer is $\mathbf{( E )}$ as can be deduced from the following drawing.
![](https://cdn.mathpix.com/cropped/2024_04_17_23f072eac9b2d02bc457g-1.jpg?height=216&width=1092&top_left_y=2177&top_left_x=457)