Finding areas the dog can wander.

Question

A dog is tied to the corner of a square hut by a rope which is 8m long. The hut measures 6m on each side. What is the area the dog can wander outside the hut?

Answer 1

Answer 2

The rope is longer than the side of the hut, so the dog can wander the area on two sides of the hut in the shape of a sector with 270° and radius 8m. The dog can still turn around to wander a quarter circle with radius (8-6) = 2 on both sides of the corner it was tied. So the total areas = 270/360 • π • 8² + 2•1/4 • π • 2² = 50π

Total area the dog can wander is 50π m²

Video discussion at 3'47" of https://youtu.be/wqyQv4XXVlo?si=JmLUUOnp43omowbq