Given the functions \( f(x) = x^2 - 4x + 4 \) and \( g(x) = \sqrt{x - 2} \), determine the domain of the composite function \( (g \circ f)(x) \). Additionally, calculate the area of the rectangle formed by the roots of the quadratic equation \( f(x) = 0 \) on the x-axis and the maximum value of \( f(x) \) on the y-axis. Let's think step by step and output the final answer within \boxed{}.
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