Question 1034618
the barn is 20 by 40.
the pony is tethered to one corner of the barn.
the length of the rope is 50.
the area of a circle is equal to pi * r^2.
the length of the rope is equal to r, which is the radius of the circle.
for 3/4 of the circle, he has the full radius of the rope at his disposal.
the area covered is 3/4 * pi * 50^2 = 3/4 * pi * 2500 = 7500/4 * pi = 1875 * pi square feet.
he has 30 foot radius of a circle left that was formed from the opposite corner on the 20 foot side.
the area he can cover, that has not already been covered, is 1/4 * pi * 30^2 = 1/4 * pi * 900 = 225 * pi square feet.
he has 10 foot radius of a circle left that was form from the opposite corner on the 40 foot side.
the area he can cover, that has not already been covered, is 1/4 * pi * 10^2 = 1/4 * pi * 100 = 25 * pi square feet.
the total area he can cover is:
1875 * pi square feet plus ...
225 * pi square feet plus ...
25 * pi square feet plus ...
equals 2125 * pi square feet.
that's equal to approximately 6675.884388878square feet.
the diagram of the area he can cover is shown below:
<img src = "http://theo.x10hosting.com/2016/051601.jpg" alt="$$$" </>