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A really big cake

Since the sums of the angles are equal (C + A = K + E), we can take two of these cakes and make a parallelogram with bases 18 + 15 = 33 and 8. We can make the same figure with 22 triangles with sides 8, 10, and 18 - 15 = 3. From here use Hero's formula for triangle area to get 165*sqrt(7)/4 square feet.

Thanks to Bicho the Inhaler for this solution.

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