The diagram above shows that a semicircle is inscribed in a quarter circle while a small circle is inscribed in the semicircle. Given that \(AD=AE\) and the radius of the quarter circle is \(14\sqrt{2} \text{ cm}\), find the area of the green region above (in \(\text{cm}^{2}\)).

For your final step, use the approximation \(\pi = \dfrac{22}{7}\).

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