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## 'Curved Square' printed from http://nrich.maths.org/

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?**
Click here for a poster of this problem.