Grazing area


B.J Kim

A. Grazing area.

Farmer Jones had a goat on a tether. He tied the end of the tether not attached to the goat to a stake in a field. Over what area could the goat graze?

Of course you need to know something about the length of the tether and about the field.

There are two structures in the field:

-- a shed that is 20 ft long and 20 feet wide (square)

-- a silo that is 20 ft in diameter

The center of the shed and the center of the silo are on a line and the distance apart is 92 feet. The distance from center to center, if you wanted to use this data, is 112 feet.

The tether for the goat is 76.7 feet long. The stake to which the tether is tied is somewhere along the line of centers between the shed and the silo.

Explore the area over which the goat can graze as the stake is moved along this line segment from the midpoint of the side of the shed to the edge of the silo.



Case 2

In the fist picture, the yellow rectangle would be the case 2

So, 92* (76.7*2)=14112.8



The total area that the goat can graze is (case1) +(case 2) + (case3).

Therefore, maximum area that the goat can graze is approximately 7911.91+ 14112.8 + 7464.71 =29489.42(ft)