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Basically we are looking at the sum of these 2 shapes.
They are both quarter circles minus triangle. 
So area is

Big leaf = pi * 6 * 6 / 4 - 6 * 6 / 2 = 9pi - 18
Small leaf = pi * 4 * 4 / 4 - 4 * 4 / 2 = 4pi - 8
Shaded region area is 13pi - 26 = 14.82 cm2.
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