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Side of square = \sqrt{652} \text{ or }25

Area of rhombus = base \times height

Now, square and rhombus share the same side CD = 25 from earlier

Thus, 500 = 25 \times height or height of rhombus = 20

Now, draw a perpendicular from D to side EF(Let call this O) and find the area of triangle DOF

Also, we know that in rhombus all side are equal or equal to 25 and height = 20, Therefore in triangle DOF by Pythagoras theorem: 25^2 = 20^2 + \text{OF} or OF =15, thus area of DOF will be \frac{1}{2}\times15\times20 =150

Area of Shaded region = Area of Square -(area of rhombus - area of triangle DOF)

Area of Shaded region = 625 -(500 -150) or 275