Insufficient Information in Geometry? (Part 2)

$\triangle ABC$ with $AB = 12 \space \text{cm}$ . A semicircle is drawn with $AB$ as the diameter. This semicircle intersects with $BC$ in $E$ . A quarter circle is drawn with $C$ as the center and $AC$ as the radius. This quarter circle intesects with $BC$ in $D$ . If the area of trapezoid $ABFC$ is $224 \space \text{cm}^{2}$ , find the total area of the red and orange region (in $\text{cm}^{2}$ ).

Give your answer to two decimal places. You may use $\pi \approx 3.14$

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