The points $P$, $Q$, $R$, $S$ lie in order along a straight line, with $PQ=QR=RS=2\;\mathrm{cm}$. Semicircles with diameters $PQ$, $QR$, $RS$ and $SP$ join to make the shape shown below.
What is the area of the shape?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.