A dog is attached to a 2121-foot rope fastened to the outside corner of a fenced-in garden that measures 1818 feet by 2323 feet. Assuming that the dog cannot enter the garden, compute the exact area that the dog can wander.

Question

A dog is attached to a 2121​-foot rope fastened to the outside corner of a​ fenced-in garden that measures 1818 feet by 2323 feet. Assuming that the dog cannot enter the​ garden, compute the exact area that the dog can wander.

oobleck · Answer

Draw the figure. The dog can wander in 3/4 of a circle of radius 2122
and also, after it wraps past the short side of the fence, a 1/4 circle of radius 303.

So the total play area is 3/4 * π * 2121^2 + 1/4 * π * 303^2

A dog is attached to a 2121​-foot rope fastened to the outside corner of a​ fenced-in garden that measures 1818 feet by 2323 feet. Assuming that the dog cannot enter the​ garden, compute the exact area that the dog can wander.

A dog is attached to a 2121-foot rope fastened to the outside corner of a fenced-in garden that measures 1818 feet by 2323 feet. Assuming that the dog cannot enter the garden, compute the exact area that the dog can wander.