How do you solve for the central area of a polygon?

Getting the central area of a polygon is not possible. Probably the question refers to the central angle. In a a regular polygon, getting the central angle is that you need to use the formula.

Central Angle of a polygon = 360 degrees / number of sides of a polygon.
Why 360 degrees? Because, a circle has a total of 360 degrees. And a circle is a polygon with no sides.

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