Acircle inscribed in a rhombus whose diagonals are 30 cm in 40 cm find the area between the rhombus and the circle

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

Using the rise/run rule. you would get 2/6.simp. 1/3