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

Answer 1

Using area of regular Polygon, the perimeter of the total grazing area of regular polygon is 100 feet and the cost to place a fence around the entire grazing area is $795.

According to the 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.

• In part 1 we asked to find the total perimeter of the grazing area using below polygon formula

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

Where a is apothem and p is the perimeter.  

500 = 10 x p/2  

1,000 = 10 x p  

100 = p

Hence the perimeter of regular polygon the total grazing area is 100 feet.  

• In part 2, 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

Now cost of fencing 1 foot = $7.59  

So, cost of fencing 100 feet = 7.59 x 100 = 759

Hence, the cost to place a fence around the entire grazing area of polygon is $795.

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