|Slice Area||=||0.5 r2|
|Total Area||=||2 r2|
A quadrilateral is a polygon with 4 sides, and the sum of its interior angles is 360 degrees. A regular quadrilateral is also called a square.
The values in the table above assume a regular polygon as in the picture. In a regular polygon, all angles and sides are equal, which means that a perfect circle can be drawn across all the vertices. The radius of this circle is called the circumradius, and is denoted r in the calculations above.
The more sides the regular polygon has, the more similar to a circle it becomes. As a result, the circumference gets closer and closer to 2 × π × r (≈ 6.283 r), and the area gets closer and closer to π × r2 (≈ 3.1415 r2).
Here are all the polygons with twenty or less sides: