A \(\large 12\) feet high room is \(\large 40\) feet long and \(\large 10\) feet wide. Brilli the ant is standing in the middle of one of the walls (which is \(\large 10\) by \(\large 12\) feet), such that it is 1 foot above the floor, and is equidistant from the other \(\large 2\) edges of that wall.
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In the middle of the wall opposite to Brilli's, rests a sugar crystal, one foot below the ceiling. The minimum distance Brilli needs to cover to reach the sugar crystal, assuming that Brilli can walk anywhere inside the room, is \(\large x\). Determine the value of \(\large x^2\).

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