You need to create a fenced off region of land for cattle to graze. The grazing area must be a total of 500 square feet, surrounded by a fence, and in the shape of a regular polygon. Within this grazing area, the length of the apothem must be 10 feet long. Part I. Find the total perimeter of the grazing area. Part II. If the cost of the fence is $7.95 per linear foot, how much will it cost to place a fence around the entire grazing area? Part III. Suppose this grazing area is of an industrial grazing area for a major industry farm. What is the total cost to build a fence around the entire land of the large scaled farm? Include all of the necessary calculations in your final answers for Parts I, II, and III.

the area of a polygon is A=perimeter×apothem÷2

you know A=500 and apothem = 10\

500=P×10/2

you should get that the perimeter is 100 from the algebra

part 1 is 100, the perimeter is 100

The 100 * 7.95

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lillian1805 lillian1805 · Answer 2 · 2021-05-03T17:43:12+02:00

Answer:

Part 1: The perimeter of the 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 $45, 540.

Step-by-step explanation:

The formula of the area of regular polygon = ap/2

Where a is apothem and p is the 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 = 10ft.

So, 500 = 10 x p/2

1,000 = 10 x p

100 = p

Part 1: Hence the perimeter of the total grazing area is 100 feet.

Now cost of fencing 1 foot = $7.59

So, cost of fencing 100 feet = 7.59 x 100 = 7.59

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, x/60 = 500

x = 500 x 60

x = 30,000

So, the area of large-scaled far is 30000 sq. ft.

Area = ap/2

So, a = 10 feet

So, 30,000 = 10p/2

60,000 = 10p

6,000 = p

Cost of fencing 1 foot = $7.59

So, cost of fencing 6000 feet = 7.59 x 6,000 = 45,540

Part 3: Hence the total cost to build a fence around the entire land of the large-scaled farm is $ 45540.