(i) The area of the playground can be found by subtracting the areas of the triangles and trapezium from the rectangle:

\(Area of rectangle ABCD = 2400 m².\)

Area of triangle AXC = \(\frac{1}{2} \times 40 \times (60 - 2x) = 20(60 - 2x)\).

Area of triangle DYB = \(\frac{1}{2} \times 60 \times (40 - x) = 30(40 - x)\).

Area of trapezium AXYD = \(x \times 30\).

Thus, the area of the playground is:

\(A = 2400 - 20(60 - 2x) - 30(40 - x) - 30x\)

\(A = x^2 - 30x + 1200\).

(ii) To find the minimum area, we differentiate \(A\) with respect to \(x\):

\(\frac{dA}{dx} = 2x - 30\).

Setting \(\frac{dA}{dx} = 0\) gives:

\(2x - 30 = 0\)

\(x = 15\).

Substituting \(x = 15\) into the area formula:

\(A = 15^2 - 30 \times 15 + 1200 = 975\).

Thus, the minimum area of the playground is 975 m².