Area of the Grazing Cow

[Mooch22]

Problem: A cow at C is tethered to a post alongside a barn 10 meters wide and 30 meters long. If the post is 10 meters from a corner of the barn and if the rope is 30 meters long, find the cow's total grazing area to the nearest square meter.





(I'm new to this site, and I'm not sure of the procedures, and I don't know how to draw images)

Are you suppose to act as if there is a circle with a radius of 30 m. and find the area of the circle and then take half of that?

 

[pka]

From your description, the post could be many different places.
If one were to draw the line segment from the post to the corner, would it be parallel to either side of the barn? If so, which side? If not, then describe the exact location of the post.

 

[stapel]

Draw a rectangle for the barn. Label the long side as "30" and the short side as "10". Draw a dot, one-third of the way from one corner to the next, along the long side. Label this as "C".

Draw the half-circle that the cow can graze along that side of the barn. What is the area?

On the short side further to C, what will be the length of rope remaining free when the cow turns the corner? This gives you the radius of the quarter-circle that the cow can graze along that side. Can the cow continue on around the side to reach the back of the barn?

On the short side closer to C, what will be the length of rope remaining free when the cow turns the corner? Can the cow continue on around the side to reach the back of the barn?

Find the areas of the half-circle and the various quarter-circles. Sum to get the total area.

Eliz.