Area of a region in polar coordinates

I’ve plotted two polar curves.

PolarPlot[{3 Sin[t], 1 + Sin[t]}, {t, 0, 2 Pi}, PlotRange -> {-1, 3}]

NLTMi Area of a region in polar coordinates

I’d like to shade the region that lies inside the circle but outside of the cardioid. Then I’d like to find the area of the shaded region using Mathematica’s Area command.

Is this possible using polar coordinates? Can someone share some suggestions?

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