see the attached figure to better understand the problem
The diagonals of a rhombus are perpendicular, so ABO is a right triangle with right angle at the center O.
applying the Pythagorean theorem
AB²=20²+15²---------> AB²=625-------> AB=√625------> AB=25 cm
I use similar triangles to get
x/20=15/25-----------> x=20*15/25------------> x=12 cm
the radius of a circle is x=12 cm
[area of a rhombus]=(30*40/2)-----> 600 cm²
[area of a circle]=pi*r²----> pi*12²----> 452.16 cm²
[the area between the rhombus and the circle]=600-452.16---> 147.84 cm²
the answer is
147.84 cm²