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Solving the problem of shadow area in primary school mathematics
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The areas of these four shadows must be equal, and the line I drew divides this part into two parts equally.

So the area of a semicircle minus the area of a triangle is the area of a shadow =0.5*π*2*2-0.5*4*2=2π-4.

So the total area of the shaded part is 8π- 16.