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Building Tetrahedra Ladder and Cube Areas and Ratios


Stage: 4 Short Challenge Level: See all short problems arranged by curriculum topic in the short problems collection
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? 

This problem is taken from the UKMT Mathematical Challenges.