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Australian AMC 2020 - Intermediate Question 27

AMC AUSTRALIA · Australian AMC 2020 - Intermediate

Question 27

A square of side length 10 cm is sitting on a line. Point $P$ is the corner of the square which starts at the bottom left, as shown. Without slipping, the square is rolled along the line in a clockwise direction until $P$ returns to the line for the first time.
To the nearest square centimetre, what is the area under the curve traced by $P$?

Question illustration