+4609 Chuck the llama is tied to the corner of a \(2\text{ m}\) by \(3\text{ m}\) shed on a \(3\text{ m}\) leash. How much area (in square meters) does Chuck have in which to play if he can go only around the outside of the shed?
+222 area of rectangle=length*width
area of rectangle=3*2
area of rectangle=6m^2
area of circle=π*r^2
area of circle=π*3^2
area of circle=π*9
area of circle=28.27433388m^2
area of circle - area of rectangle= area around the outside of the shed
28.27433388m^2-6m^2=22.27433388m^2
+198 Chuck can play in the three quarters of the circle with radius 3 that does not have any area inside the shed.
The area of that is \(\frac {3}{4} \times9 \pi = \frac{27\pi} {4}\).
One meter of Chuck's rope can extend below the shed on the bottom right corner with one meter left. So, Chuck has a quarter circle with radius \(1\) he can play in.
The total is \(\frac{27\pi} {4} + \frac{\pi}{4}= \frac{28\pi}{4} = \boxed{7\pi}\) .
