Calculating the area of polygons requires specific formula, while calculating perimeters simply involves the addition of all sides of a polygon. Calculating the perimeter or area of circles and other monogons involve formulas that use the mathematical concepts of pi and radius to reach a result.

Polygons are shapes with more than one side, such as triangles and squares, while monogons are shapes without multiple sides, such as circles and ellipses. The perimeter of circles and related monogons cannot be calculated by adding the lengths of all sides, as monogons have only one. To calculate the perimeter of a circle, the formula is two multiplied by pi multiplied by the circle's radius. Calculating the perimeter of ellipses, or non-perfect circles, involves much more complex formulas.

Calculate the area of any regular polygon, a shape with all sides of equal length and all angles of equal measure, by the perimeter of the shape multiplied by its apothem, divided by two. The apothem measures the distance from the center of the polygon to one of its sides.

Calculate the area of a perfect circle by multiplying the circle's radius raised to the second power, or multiplied by itself. Determine the area of an ellipse by multiplying the semimajor and semiminor axes by pi. The semimajor axis measures half the distance of the longer of the ellipse's axes, while the semiminor measures half the distance of the smaller of the ellipse's axes.