In this case one of the solutions is a square, with area 1/2, however infinitely many other orthodiagonal quadrilaterals with unit-length diagonals also have diameter one and have the same area as the square, so in this case the solution is not unique.
One of the solutions is a square infinitely many other orthodiagonal quadrilaterals with unit-length diagonals also have diameter one and have the same area as the square, so in this case the solution is not unique. This is with area 1/2. This is in this case. This is however.