ABCD is a square . Another square EFGH with the same area is placed on the square ABCD such that the point of intersection of diagonals of square ABCD and square EFGH coincide and the sides of square EFGH are parallel to the diagonals of square ABCD. Thus a new figure is formed as shown in the figure . What is the area enclosed by the given figure if each side of the square is 4 cm :

Options

A. `32(2-sqrt2)`
B. `16((3+sqrt2))/(2+sqrt2)`
C. `32((2+sqrt2))/(3+sqrt2)`
D. none of these

Answer

A