In a large and flat grass field, there is a 30x30 feet square barn facing due North. Straight from the NorthEast corner of the barn is a fence running due East 40 feet long. There is a horse tied on the SouthEast corner of the barn with a rope that will allow him to eat grass in any direction up to 100 feet. The horse can't eat under the barn, and the rope can't pass through the barn or through the fence. The horse can walk around the barn or the fence, but is limited by the length of the rope.

How many square feet of grass can the horse reach?

(I found this problem pretty interesting, but I am not the author and have no idea who is the author).

(In reply to exact answer by John Reid)

According to my calculator 7875pi + 600 + 400sqr(6) + 3750atan(3/4) - 1250atan(8sqr(6)/29) - 800atan(2sqr(6)/5) comes out to 86490.0418758046

... whoops!, sorry: my calculator was in degree mode and should have been in radian mode. It checks out once in radian mode.

Edited on April 6, 2005, 4:17 pm

Posted by Charlie on 2005-04-06 16:12:51