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13 May, 07:16

Find the area of an inscribed 100-gon if the radius of the circle is 1 unit.

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  1. 13 May, 07:27
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    A polygon inscribed in a circle, luckily, has a derived formula already. It is:

    A = (nr²/2) [sin (360/n) ]

    where n is the number of sides of the polygon and r is the radius of the circle. For this problem, n = 100 and r = 1. Substituting this to the equation,

    A = (100 (1) ²/2) [sin (360/100) ]

    A = 3.14 square units

    Thus, the 100-gon has an area of 3.14 square units.
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