Question 712653
The goat can pull the rope straight, adjascent to one side of the corner, and can move at that distance from the corner to pulling the rope adjascent to the other side of the corner, covering 270 degrees of a circle with radius 15 feet, the length of the rope.  


The area is {{{(270/360)*pi*15^2}}} feet^2


The goat while at either side with rope against that side, can move 1/4 of a circle at radius 15-10=5 feet.  There are two of these, one for each side of the corner at which the goat is tethered.


These two smaller parts are {{{2*(90/360)*pi*5^2}}} feet^2


The sum of all of these areas is {{{highlight((270/360)*pi*15^2+2*(90/360)*pi*5^2)}}} ft.^2