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# What is a Polygon?

Maths | 7-14 yrs | Learning Pod, Reading Pod

## Polygon : Definition

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

### Characteristics of a Polygon

1. Multiple angles.
2. A closed (all lines connect up) plane (two dimensional shape with zero thickness) shape.
3. Has at least three sides (with straight lines called line segments and no curves).
4. 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

1. 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.
2. If the lines of a polygon intersect they are complex polygons and if they don’t intersect they are simple polygons.
3. A regular polygon has equilateral sides and angles; whereas an irregular polygon has uneven sides and angles.
4. 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.