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 1. Find the total perimeter of the grazing area. Part 2. If the cost of the fence is $7.95 per linear foot, how much will it cost to place a fence around entire grazing area? Part 3. Suppose this grazing area is 1/60 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?

Answer 1

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 = $\frac{ap}{2}$

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,  $500=\frac{10 \times p}{2}$

$1000=10 \times p$

$100= p$

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 = $7.59 \times 100 = 759$

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, $\frac{x}{60}= 500$

$x= 500\times 60$

$x=30000$

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

now ,Area = $\frac{ap}{2}$

So, a = 10 feet

So, $30000=\frac{10p}{2}$

$60000=10p$

$6000=p$

Cost of fencing 1 foot = $7.59

So, cost of fencing 6000 feet = $7.59 \times 6000 = 45540$

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

Answer 2

A.
the area of a polygon is/
A= perimeter X apothem /2
A=500
apothem = 10
500 = (P * 10)/2
P =100

B. 100*7.95 = $795

C.
60*100= 6,000
6,000 * $7.95=
$47,520