I assume you mean a polygon inscribed in a circle. It is regular if all its sides and angles are equal.
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Unless the area is a regular polygon (or a circle) you cannot.
The circle has a smaller area than the polygon.
No because a regular polygon has equal sides and equal interior angles
circumscribed means the polygon is drawn around a circle, and inscribed means the polygon is drawn inside the circle. See related links below for polygon circumscribed about a circle and polygon inscribed in a circle.
what is the name of a smooth curved line around the outside of a regular polygon