[cardinopolynomial]

$2\pi r^2+\pi R^2=150$
$2r^2+R^2=\frac{150}{\pi} $
$(R-r)^2+x^2=(R+r)^2$
$x=2\sqrt{Rr} $
$(2R-r)^2=4Rr+r^2$
$4R^2-8Rr=0$
$R(R-2r)=0$
$R=2r$
$\frac{R^2}{2}+R^2= \frac{150}{\pi} $
$R^2=\frac{100}{\pi}$
$Area=2\times \pi\times\frac{100}{\pi}$
Area=200 ตารางหน่วย