divdude, Let us consider a unit cube lying on a plane on one of its faces. When a vertical plane passing through a diagonal of the cube's horizontal faces is slowly rotated about a line that is parallel to the diagonal but passes through the center of the cube, a time will come when the intersection points of the plane and two pairs of diagonally opposite edges of the cube will exactly form a square. This will be the largest square that can be inscribed in the cube. If the plane intersects each of these edges at a distance of x from the diagonally opposite vertices of the cube, then for the intersection to be a square, x^2 + x^2 = (1-x)^2 + (1-x)^2 + 1 which implies x = 3/4. The length of each side of the square is then (3/4)*(2)^0.5. So the square's area will be 9/8.