Insufficient Information in Geometry? (Part 2)

Geometry Level 5

\(\triangle ABC\) 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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