SOLUTION: if the sum of the interior angles of a regular polygon is 720 (degree) and the perimeter of that regular polygon is 72 feet, then what is the area (in square feet) of that polygon?

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Question 507483: if the sum of the interior angles of a regular polygon is 720 (degree) and the perimeter of that regular polygon is 72 feet, then what is the area (in square feet) of that polygon?
Answer by stanbon(75887) (Show Source):
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if the sum of the interior angles of a regular polygon is 720 (degree) and the perimeter of that regular polygon is 72 feet, then what is the area (in square feet) of that polygon?
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(n-2)180 = 720
n-2 = 4
n = 6 sides
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72/6 = 12 feet (length of each side
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Sum of exterior angles = 360
Each of the 6 exterior angles = 360/6 = 60
So each of the interior angles is 180-60 = 120
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So each pie-shaped interior regular triangle is 60-60-60
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Knowing all that you should be able to find the area
of each of the interior triangles; then multiply by
6 to get the total interior area.
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Cheers,
Stan H.