## Polygon : Definition

A polygon is a closed shape with three or more straight sides and angles.

### Characteristics of a Polygon

- Multiple angles.
- A closed (all lines connect up) plane (two dimensional shape with zero thickness) shape.
- Has at least three sides (with straight lines called line segments and no curves).
- At least three angles (an angle is a figure formed by two sides intersecting).

## Polygon Formulae

- The point at which the two sides meet is called a vortex.
- The line segment that joins two vertices is called a diagonal. No. of diagonals= n(n-3)/2 (where n=number of sides).
- The sum of the interior angles= (n-2) * 180.

## Types of Polygons

- We classify them by the number of sides they have and we attach “gon” to its sides for polygon names. A 42 side polygon is called a 42 gon.
- If the lines of a polygon intersect they are complex polygons and if they don’t intersect they are simple polygons.
- A regular polygon has equilateral sides and angles; whereas an irregular polygon has uneven sides and angles.
- A concave polygon has at least one angle pointing inwards and is greater than 180. A convex polygon has all angles pointing outwards, no angle is greater than 180 and the diagonals do not merge outside the polygon.

## Calculating the Area of a Polygon

It is more complicated to find the area of an irregular polygon as you would have to break it up into small triangles and then calculate the area.

### Why do we need to study about Polygons?

Polygon shapes are important for architects, farmers, engineers, artists etc. You need polygons even when you’re planning a party.

### Technical Facts about Polygons

The circumcircle of a regular polygon is the circle whose points touch each vertex of the polygon.

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