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6 December, 17:42

The central angle of a regular polygon is 18 degrees. Th e perimeter of the polygon is 144 ft. What is the area of the polygon to the nearest tenth?

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  1. 6 December, 17:53
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    Given that the central angle of a polygon is 18, then the number of sides of the polygon will be:

    360/18

    =20 sides

    thus the side length will be:

    144/20

    =7.2 ft

    hence the area will b given by:

    p=s*n

    a=s/[2tan (180) / n]

    where:

    Area = (a*p) / 2

    p=perimeter, s=side length, n=number of sides

    p=7.2*20=144

    a=7.2/[2tan (180/20) ]=22.73

    thus

    A = (144*22.73) / 2

    A=1632.524 ft²
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