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Consider a regular polygon $A_1A_2....A_n$ of n sides with unit side length.Without loss of generality we can take $A_1$ coincident with the origin O and $A_2$ on positive x axis s.t. $A_1A_2=1$.If $D$ in the region in the polygon with the property that each of the points of $D$ is closer to the centre of the polygon than to any of the $n$ sides ,it is required to find the equation and the area of $D$ .Lots of thanks in anticipation of help

AgnostMystic
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  • The boundary of region $D$ is the n-sided regular polygon obtained by shrinking (applying an homothety) in a ratio 1/2 the initial polygon. Thus the ratio of areas is 1/4. It remains to compute the area of a regular polygon with unit side... – Jean Marie Sep 22 '17 at 23:02

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