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

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 = \(\dfrac{1}{6}\)\(\pi\)2² = \(\dfrac{2\pi}{3}\)

^{=> S = 4\(\sqrt{3}\)} - 3\(\dfrac{2\pi}{3}\) = 4\(\sqrt{3}\) - 2\(\pi\)