Challenge Level

A square of side length 1 has an arc of radius 1 drawn from each of its corners, as in the following diagram. The arcs intersect inside the square at four points, to create the shaded region.

**What is the area of the largest square that can be completely contained within the shaded region?**

Is this a good estimate of the actual shaded area?

**What is the exact area of the central shaded region?**

How did that compare to your estimate?

**Can you find more than one method to work out the exact area?**

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