Question

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.

Answer 1

Answer: Part I: 100

Part II: $795

Part 3: 47,700

Step-by-step explanation:

First, to find the total perimeter of the grazing area, you would need to set up an equation to find the perimeter.  

Area = perimeter * apothem / 2.  

Fill in the known values: 500 = P * 10/2. 10 divided by 2 is 5, and 500 divided by 5 is 100. P = 100

To find the cost to place a fence around the total grazing, multiply 7.95 by 100 to get 795.

To solve for the third part, set up a proportion: 1/60 = 100/x

Cross multiply: X = 6,000

Multiply 6000 and 7.95 to get 47,700. $47,700 is the total cost.

Answer 2

Part 1 : A=1/2 ap  P= 2A/a = 1000/10 = 100 ft.
​Part 2 : (100 ft.)($7.95/ft) = $795
​I'm not sure for part 3.