A geometry problem by Kaleem Kħặŋ

By pythagorean theorem: $(2x)^2=9^2+9^2$ $\implies$ $4x^2=81+81$ $\implies$ $x^2=\dfrac{81}{2}$ $\implies$ $x=\sqrt{\dfrac{81}{2}}=9\sqrt{\dfrac{1}{2}}$

$Area~segment=area~sector-area~triangle=\dfrac{90}{360}\pi \left(9\sqrt{\dfrac{1}{2}}\right)^2-\dfrac{1}{2}\left(9\sqrt{\dfrac{1}{2}}\right)^2=11.5586$

$Area~shaded=area~semicircle+area~segment=\dfrac{1}{2}\pi (4.5^2)+11.5586=$ $\boxed{43.367}$