Consider all configurations where the White Queens are located in the follow\
    ing two pengagons

                      inside the unit square [0,1]x[0,1]



      [[0, 0], [a, a], [a, a + b - e], [a - e, a + b - e], [0, b], [0, 0]]



                                      and



[[v0, 0], [v0 + c, 0], [v0 + c, c - 2 f + d], [v0 + c - f, c - f + d], [v0, d],

    [v0, 0]]



             then the Black Queens are located in the two pentagons



[[v0, 1], [a, 1], [a, v0 + 2 c - 2 f + d - a],

      v0                        v0
    [---- + d/2 - b/2 + c - f, ---- + d/2 + b/2 + c - f], [v0, v0 + b], [v0, 1]
      2                         2

    ]



                                      and



[[1, 1], [v0 + c, v0 + c], [v0 + c, a + b - e], [a + b - e + v0 - d, a + b - e],

    [1, 1 + d - v0], [1, 1]]

                     The area of the White Queens region is



                                  2            2
                                 e            c      2
                          a b - ---- + c d + ---- - f
                                 2            2



                   and the area of the Black Queens region is



                               2               2
                            3 c            7 v0    v0 b           2
-d + 2 v0 - a - a b - c d - ---- + 2 c f - ----- - ---- + a v0 - a  + 2 a d
                             2               4      2

                                  2
                       3 b d   3 b                  v0 d
     + 3 a c - 2 a f + ----- - ---- + 2 b c - b f + ---- - 2 v0 c + v0 f + f d
                         2      4                    2

          2                             2
       3 d                             e      2
     - ---- + a e + b e - e d - e c - ---- - f
        4                              2



Optimally, these should be the same. Maximizing them under this constaint sh\
    ows that

                     the maximal area (for each of them) is



                                      7/48



and it is achieved with the following configuration for White followed by Bl\
    ack



[[[[0, 0], [1/4, 1/4], [1/4, 1/2], [1/6, 1/2], [0, 1/3], [0, 0]],

    [[1/2, 0], [3/4, 0], [3/4, 1/4], [2/3, 1/3], [1/2, 1/6], [1/2, 0]]], [

    [[1/2, 1], [1/4, 1], [1/4, 3/4], [1/3, 2/3], [1/2, 5/6], [1/2, 1]],

    [[1, 1], [3/4, 3/4], [3/4, 1/2], [5/6, 1/2], [1, 2/3], [1, 1]]]]