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Purple Comet 2016 MS Problem 10

Source:

April 13, 2018
Purple Comet

Problem Statement

Mildred the cow is tied with a rope to the side of a square shed with side length 10 meters. The rope is attached to the shed at a point two meters from one corner of the shed. The rope is 14 meters long. The area of grass growing around the shed that Mildred can reach is given by nπn\pi square meters, where nn is a positive integer. Find nn.