The curve $C$, which is a type of cardioid, is given by

where $0\le t<2\pi$.

The cardioid intersects the $y$ axis at the points $P$ and $R$, and the $x$ axis at $S$.

The tangents to the cardioid at $P$ and $R$ intersect at the point $Q$.

Find the area of the quadrilateral $PQRS$.

Give your answer below, to three significant figures where necessary.