Geometry Formulas for Polygons

The following symbols are used in these polygon formulas:

    K = area

    r= radius of inscribed circle

    R = radius of circumscribed circle

    p and q are diagonals

    n= number of sides

    θ = one of the vertex angles

Polygon

A polygon is a two-dimensional geometric figure that is formed by connecting a sequence of straight line segments to create a closed shape. The segments are called sides, and the points where the sides intersect are called vertices. Polygons can have any number of sides, but they must have at least three sides.

The word "polygon" has its origins in the Greek words πολύς ("many") and γωνία (gōnia), meaning "knee" or "angle."

Polygons are classified based on the number of sides they have:

Triangles: Triangles are polygons with three sides and three vertices. They are further classified into:

Equilateral triangle: All three sides are equal in length. Isosceles triangle: Two sides are equal in length. Scalene triangle: All three sides have different lengths. Right triangle: One angle is a right angle (90 degrees). Quadrilaterals: Quadrilaterals are polygons with four sides and four vertices. They include:

Square: All four sides are equal in length, and all angles are right angles. Rectangle: Opposite sides are equal in length, and all angles are right angles. Parallelogram: Opposite sides are parallel and equal in length. Rhombus: All sides are equal in length. Trapezoid (or trapezium): One pair of opposite sides is parallel. Pentagons: Pentagons have five sides and five vertices.

Hexagons: Hexagons have six sides and six vertices.

Heptagons: Heptagons have seven sides and seven vertices.

Octagons: Octagons have eight sides and eight vertices.

And so on...

Polygons can also be classified as regular or irregular. Regular polygons have all sides and angles equal in measure, while irregular polygons have sides and/or angles of different lengths or measures.

The sum of the interior angles of any polygon can be found using the formula: (n-2) * 180 degrees, where n is the number of sides.

 Source: CRC Standard Math Tables, 1987