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The length of each s is an integer => The shortest length is 1 inches
It is not possible to make a triangle out of any three ss => Total length of 2 ss is less than or equal to length of next s.
The length of the first 2 ss: 1 inches
The length of the next s: Total length of 2 ss before.
=> sequence: 1  1  2  3  5  8  13  21  43  55
=> The longest s could possibly: 55 inches

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Center of the circle: ABC
=> AB = BC = AC = 2R = 4
=> ABC is a equilateral triangle
The area for the shaded region: S
The area for a sector definition by A and 2 tangential points: S_{A}
S = S_{ABC } 3S_{A}
S_{ABC} = \(\dfrac{1}{2}\).4.4.\(\dfrac{\sqrt{3}}{2}\) = 4\(\sqrt{3}\)
S_{A }= \(\dfrac{60}{360}\)S_{circles }= \(\dfrac{1}{6}\)\(\pi\)2^{2 }= \(\dfrac{2\pi}{3}\)
^{=> S = 4\(\sqrt{3}\)}  3\(\dfrac{2\pi}{3}\) = 4\(\sqrt{3}\)  2\(\pi\)