Geometry + Radical Arithmetic = Headache!

Geometry Level 5

Consider a square ABCDABCD with side of length 44.

Let EE be a point outside ABCDABCD such that ΔCDE\Delta CDE is equilateral.

Draw CEK=30\angle CEK = 30^\circ such that ray EKEK intersects ray ACAC at GG, ray DCDC at FF, ray ABAB at PP.

If Area of ΔAGP\Delta AGP can be represented as:

a+bca + b\sqrt{c} where cc is independent of a perfect square.

Find a+b+ca + b + c.

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