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Basics of Polygons

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A plane figure bounded by straight lines is called a rectilinear figure and any closed rectilinear figure is called a polygon.

Types of polygons

Equiangular Polygons: If all the angles of a polygon are equal, then it is called an equiangular polygon.

Equilateral polygon: If all the sides if a polygon are equal, then it is called an equilateral polygon.
Note: Except for triangles, an equilateral polygon need not necessarily be an equiangular polygon and vice versa.



Regular Polygon: If all the sides and all the angles of a polygon are equal, then it is called a regular polygon.



Here, ABCDEF is a regular polygon.
AB = BC = CD = DE = EF = FA and also all the interior angles are equal.

Convex polygon: 
If all the interior angles of a polygon are less than 180o, then it is called a convex polygon.

Concave polygon:
If one or more of the interior angles of a polygon are reflex angles, i.e. greater than 180o, then it is called a concave polygon.

Names of polygons based on the number of sides:
3 - Triangle
4 - Quadrilateral
5 - Pentagon
6 - Hexagon
7 - Septagon or Heptagon
8 - Octagon
9 - Nonagon
10 - Decagon

Properties of polygons

1. A diagonal of a polygon is the straight line which joins any two non-adjacent vertices of the polygon.
2. An exterior angle is obtained when any one side of a polygon is extended or produced.
3. Unless otherwise stated a polygon typically means a convex polygon.
4. In a polygon of n sides, the sum of interior angles is equal to (n - 2) x 180o.
5. In a polygon of n sides, the sum of exterior angles is equal to 360o.
6. At each vertex of a polygon, exterior angle + interior angle = 180o.
7. Area of a regular hexagon = 6 times the area of an equilateral triangle with the length of the side same as that of the regular hexagon.


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