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Quadarc

Age 14 to 16
Challenge Level

square ABCD of sides 10 cm, with 4 quadrants of radius 10cm constructed using the corners of the square as centres.

Given a square $ABCD$ of sides $10$ cm, and using the corners as centres, construct four quadrants with radius $10$ cm each inside the square. The four arcs intersect at $P$, $Q$, $R$ and $S$. Find the area enclosed by $PQRS$.