What is the relationship between the radius of the unshaded semicircle and the area of the shaded shape?

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The first table shows the calculations used to find the area of the shaded shape.

The second table calculates the area of the shaded shape with the theoretical relationship between the radius of the semicircle and the area of the shaded shape.

This shows that the relationship between the radius of the semicircle (n) and the area of the shaded shape (r) is r=6n2.