Polygon Formula

About Polygon Formula

Let's review the definition of a polygon before moving on to the polygon formula. A polygon is a two-dimensional closed object with three or more straight lines. At least three sides are required for a polygon. At the vertex, each side of the line segment intersects with another line segment. Get the List of all Maths formulas in one place.

Types of Polygon

A polygon is categorised into the following categories based on its angle measure and sides:

  • Regular Polygon – All interior angles and the sides are of the same measure
  • Irregular Polygon – All interior angles and the sides have different values
  • Convex polygon – All interior angles of polygon < 180 degrees
  • Concave Polygon – Polygons that have 1 or more interior angles with a measure of >180 degrees

Formula: Area in terms of the perimeter,

Area=(Perimeter × Apothem)2

in which perimeter = number of sides × length of one side

A polygon's shape is determined by its number of sides, and it is named after that number. Triangles, squares, pentagons, hexagons, and other polygons are common examples. The polygons are given below in order of their number of the sides.

polygon

What is Polygon Formula?

  • Formula : For a regular 'n' sided polygon, sum of interior angles of a polygon is 180°(n-2)
  • Formula :Number of diagonals of an “n-sided” polygon = [n(n-3)]/2
  • Formula : Measure of the each interior angle of a regular n-sided polygon = [(n-2)180°]/n
  • Formula : Measure of the exterior angles of a regular n-sided polygon = 360°/n
  • Formula 5: Area of regular polygon = (number of sides × length of the one side × apothem)/2, where, length of apothem is given as the
  • l/2tan(180/n) and where l is side length and n is the number of sides of the regular polygon.

polygon

Properties of Polygon

The important properties of the polygon are

  • Sum of interior angles of all the quadrangles = 360°.
  • If at least 1 of the interior angles > 180 degrees, then it is called a concave polygon.
  • If a polygon does not cross over itself & has only 1 boundary, it is called a simple polygon. Otherwise, it is a complex polygon.

Find pdf of Polygon Formula

Polygon Formula
Polygon Formula

Related Links

Frequently Asked Questions on Polygon Formula