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Two circles of radius r fit inside a square of side length s.  Find r in terms of s, and then find the area of the shaded region in terms of s.

 

 Feb 16, 2021
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Connect the centers of the circles. You will get a line of length 2r.

You can also draw a line starting at the center higher circle going downward and a line starting at the center of the lower circle to form an isosceles right triangle with hypotenuse 2r.

The side length of a leg of the isosceles right triangle is \(r\sqrt{2}\).
Therefore, the side length (s) = \(2r + r\sqrt2\).

 Feb 16, 2021

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