I need to find the length measurement of each side of a regular polygon to the nearest foot considering the following:

The polygon has an apothem of 80 feet
The polygon has 20 sides
The area of the polygon is 20,000 square feet
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13 Answers

Area of a regular polygon = 1/2 (apothem) (perimeter)

*substitute the givens

20000 sq. feet = 1/2 (80 feet) (Perimeter)

*multiply the equation by 2

40000 sq. feet = 80 feet (Perimeter)

*divide by 80 feet

500 feet = Perimeter

 

it says that the polygon has 20 sides and the formula for the perimeter of the polygon is by adding all its sides

so,

20(length) = Perimeter

20(length) = 500

length = 25 feet

 

Therefore, the length of each side of the polygon is 25 feet.
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20000=1/2A(P)                             P=500/20 sides

20,000=1/2(80)(P)                         S=25

20,000=40P

500=P
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yes It will be a equilateral!

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