# 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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