Bigger than a circle

Calculus Level 4

The diagram above shows both a unit circle and a circle-like shape \(S\)--slightly larger than the unit circle--defined by the equation \[\sqrt{1-|x|} + \sqrt{1-|y|} = 1.\] What is the percentage by which the area of \(S\) is bigger than the area of the unit circle?

Give your answer to 3 decimal places.

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