3. (5) In the space divided into unit cubes with integer-coordinate vertices, the plane $x+y+z=0$ has been drawn. Find the values of the areas of the pieces into which it is divided by the faces of the cubes.
3. It is easy to see that the plane intersects each cube either at a vertex or at three vertices forming an equilateral triangle with side length $\sqrt{2}$. Thus, the answer: the areas of all pieces are $\sqrt{3} / 2$.