SOLUTION: Find the area of a regular 24-gon with perimeter 72. Round your answer to the nearest thousandth.

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Question 1022815: Find the area of a regular 24-gon with perimeter 72.
Round your answer to the nearest thousandth.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the area of a regular 24-gon with perimeter 72.
Round your answer to the nearest thousandth.
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Break it into 24 equilateral triangles.
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Find the area of one of those equi triangles.
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each side is 72/24 = 3
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Sketch the altitude of the triangle.
You then have 2 right triangles.
base = 1.5
hypotenuse = 3
altitude = sqrt(3^2 - 1.5^2] = 2.6
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area = (1/2)base*alt = (0.5)*3*2.6 = 3.897
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Total Area = 24*3.897 = 93.521 sq.units
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Cheers,
Stan H.
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