Equation of a certain region inside a regular polygon of $n$ .

Question

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