Answer:
Part 1: The perimeter of total grazing area is 100 feet.
Part 2: The cost of fencing the entire grazing area is $759.
Part 3: The total cost to build a fence around the entire land of the large scaled farm is $ 45540.
Step-by-step explanation:
Formula of area of regular polygon = ![\frac{ap}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bap%7D%7B2%7D)
Where a is apothem and p is perimeter.
We are given that The grazing area must be a total of 500 square feet.
We are also given that the length of the apothem must be 10 feet long.
So, area = 500 sq. ft.
a = 10 ft.
So, ![500=\frac{10 \times p}{2}](https://tex.z-dn.net/?f=500%3D%5Cfrac%7B10%20%5Ctimes%20p%7D%7B2%7D)
![1000=10 \times p](https://tex.z-dn.net/?f=1000%3D10%20%5Ctimes%20p)
![100= p](https://tex.z-dn.net/?f=100%3D%20p)
Part 1: Hence the perimeter of total grazing area is 100 feet.
Now cost of fencing 1 foot = $7.59
So, cost of fencing 100 feet = ![7.59 \times 100 = 759](https://tex.z-dn.net/?f=7.59%20%5Ctimes%20100%20%3D%20759)
Part 2: Hence the cost of fencing the entire grazing area is $759.
Let the industrial grazing area be x
Since we are given that this grazing area is 1/60 of an Industrial grazing area
So, ![\frac{x}{60}= 500](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B60%7D%3D%20500)
![x= 500\times 60](https://tex.z-dn.net/?f=x%3D%20500%5Ctimes%2060)
![x=30000](https://tex.z-dn.net/?f=x%3D30000)
So, area of large scaled far is 30000 sq.ft.
now ,Area = ![\frac{ap}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bap%7D%7B2%7D)
So, a = 10 feet
So, ![30000=\frac{10p}{2}](https://tex.z-dn.net/?f=30000%3D%5Cfrac%7B10p%7D%7B2%7D)
![60000=10p](https://tex.z-dn.net/?f=60000%3D10p)
![6000=p](https://tex.z-dn.net/?f=6000%3Dp)
Cost of fencing 1 foot = $7.59
So, cost of fencing 6000 feet = ![7.59 \times 6000 = 45540](https://tex.z-dn.net/?f=7.59%20%5Ctimes%206000%20%3D%2045540)
Part 3: Hence the total cost to build a fence around the entire land of the large scaled farm is $ 45540.