In a rectangle with a side length of \(10\) cm, two identical semicircles are drawn with their diameters coinciding with

[Gmat_mission]

In a rectangle with a side length of \(10\) cm, two identical semicircles are drawn with their diameters coinciding with the opposite sides of the rectangle. Then a circle is drawn through the points \(A, B, C,\) and \(D,\) where \(A\) and \(C\) are the intersection points of the semicircles. What is the area of the green region?\

A. \(10.5\pi-25\)
B. \(11\pi-25\)
C. \(11.5\pi-25\)
D. \(12\pi-25\)
E. \(12.5\pi-25\)

Answer: E

Source: GMAT Club Tests