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).

 The circle with the 100 ft radius would extend from due west to due east plus 53.1 degrees or 233.1 degrees.  233.1/360 would be 64.75 % of the circle  so this area would be 64.75% of 31415.9 or 20341.8 sq ft. Add this to the triangle east of barn 600 + 2341.8 = 20941.8.

West of the barn is 25% of a circle with a 70 ft radius or 3848.4 sq ft

 North of the barn is a triange with hypotenuse of 40 western angle of 44.2 degrees. North of this is a circle with 40 ft radius and 45.8 degrees 12.72 % of a 40 ft circle is 639.4 sq ft.

 The eastern tringle has hypotenuse of 50 and the eastern angle is 34 degrees Total area of the obtuse triangle is 978.2

 The remainder is circle with 50 ft radius of 92.9 degrees and 2072.6 sq ft.
 
 The  total is 28480.4 sq ft or about 1/2 acre

Posted by ollie on 2005-05-20 16:41:29