In the diagram, \(S_1\), \(S_2\) represents the area of squares \(ACDE\) and \(CFGB\) with side length \(a\) and \(b\), respectively. Given that \(A\), \(B\), \(C\) are on the same straight line, \(a^2 + b^2 = 20\), \(AB = a + b = 6\) cm, find the area of the shaded region.

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