Polygon Formulas
There are several formulas related to polygons in geometry. Some of the most commonly used ones include:
- Area Formula
- Perimeter Formula
- Number of Diagonals
All the formulas related to different polygons are discussed below:
Area of Polygons
Area of a Polygon represents the total space it occupies in a two-dimensional plane, is determined by specific formulas based on the number of sides and the polygon’s classification. The area formulas are as follows:
Area of Polygon |
Formula |
---|---|
1/2 × Base × Height |
|
Base × Height |
|
Length × Breadth |
|
(Side)2 |
|
1/2 × diagonal1 × diagonal2 |
|
1/2 × Height × Sum of Parallel Sides |
|
(5/2) × side length × Apothem |
|
Area of Hexagon |
{(3√3)/2}side2 |
Area of Heptagon |
3.643 × Side2 |
Perimeter of Polygons
The Perimeter of a two-dimensional shape represents the total length of its outer boundary. For Polygons, the Perimeter is calculated as follows:
Perimeter of Polygon |
Formula |
---|---|
Sum of Three Sides |
|
2(Sum of Adjacent Sides) |
|
2(length + breadth) |
|
4 × Side |
|
4 × Side |
|
Sum of Parallel Sides + Sum of Non-Parallel Sides |
|
Perimeter of Pentagon |
5 × Side |
Perimeter of Hexagon |
6 × Side |
Perimeter of Heptagon |
7 × Side |
Diagonal of Polygon Formula
A Diagonal of a Polygon is a line segment formed by connecting two vertices that are not adjacent.
Number of Diagonals in a Polygon = n(n−3)/2,
Where ‘n’ represents the number of sides the Polygon possesses.
Read More about Diagonal of Polygon Formula.
Polygon – Shape, Formula, Types, and Examples
Polygon in Maths is a two-dimensional shape made up of straight lines that form a closed polygonal chain. The word “polygon” comes from the words “poly” and “gon”, which mean “many” and “sides”.
Polygons can be simple or self-intersecting. A simple polygon does not intersect itself, except at the shared endpoints of consecutive segments. A polygonal chain that crosses over itself creates a self-intersecting polygon. Polygons can also be classified as concave or convex.
In this article, we have mentioned in detail about Polygons and their types, formulas, and examples.
Important Facts about Polygons |
|
---|---|
Sum of Interior Angles of Polygon |
(n–2) × 180° |
Number of Diagonals in Polygon |
n(n–3)/2 |
Interior Angle of Regular Polygon |
{(n–2) × 180°}/n |
Exterior Angle of Regular polygon |
360°/n |
Table of Content
- What are Polygons?
- Polygon Definition
- Polygon Chart based on Number of Sides
- Properties of Polygons
- Polygon Shapes
- Types of Polygons
- Polygons on the Basis of Sides
- Polygons On Basis of Angles
- Polygons On Basis of Boundaries
- Polygon Formulas
- Area of Polygons
- Perimeter of Polygons
- Angles in Polygons
- FAQs