Easy math problem [Perimeter & AREA ]

#1 Fred has a dog named spot who is tied to a 2m piece of chain inside a kennel measuring 4m by 2m. If spot's chain is attached to the middle of the longest side of the kennel what area of the inside kennel is spot unable to reach?

Post a diagram if u can somehow + detailed answer

#2 Erin is a farmer who owns 25 sheep that need to be fenced in to a four sided field. If each sheep needs 4m^2 of grass to grae on, and each meter of fence costs 5$ what is the least amount of money needed to fence in the sheep?

Same as #1

 

I got some time on my hands so ill do # 1 for you :]
1. So you are looking at a rectangle. The dog is attached by chain to the center of the longer side of the rectangle.
General Idea: Draw a circle within the rectangle and subtract the area of the circle from the area of the rectangle.
2. So you know the length of the chain is 2 meters, this is your circles radius.
3. the area of a circle is (Pi)r^2 so your circle's area is 4Pi or approx 12.56 now you want to take half of this number because only half of the circle is actually in the rectangle which is 6.28 and subtract that from the area of the rectangle which is 2*4 or 8m the final area the dog cannot reach in is 1.72meters :]

 

Thanks alot !

 

Also note when comparing perimeter and area of a 4 sided polygon, a square will always have the lowest perimeter to area.

 

25 sheep x 4 m^2 of room each = 100m^2 of room required.

100m^2 can either be a rectangle of dimension, 1 x 100, 2 x 50, 3 x 33, 4 x 25.... etc etc etc, or a square of dimension 10 x 10.

Of these, the square will have the smallest perimeter. Measuring 10m on each side, the perimeter will be 40m.
Hence, Erin will need to use 40 x 5 dollars worth of fencing. He would have to spend $200 on fencing.

 

thats loci and constructions