Irregular Polygon

A polygon is said to be irregular, if all its sides are unequal. In a irregular polygon the interior angles are also unequal.
Irregular Polygon

What is an Irregular Polygon?

A polygon is said to be irregular, if all the sides are not equal. In an irregular polygon each interior angle measures unequal.
What is an Irregular Polygon

The figure shows an irregular polygon of 7 sides (Heptagon).

1. All the regular polygons are convex polygons.

2. An irregular polygon can be concave or convex.

Irregular Polygon Shapes

Irregular polygons are classified according to the number of sides.

 Number of Sides of a Polygon   Polygon   Name of the Polygon 
 3   Triangle   Triangle
 4   Square   Square
 5   Pentagon   Pentagon
 6   Hexagon   Hexagon
 7   Heptagon   Heptagon
 8   Octagon   Octagon
 9   Nonagon   Nonagon
 10   Decagon   Decagon

11 sided polygon - hendecagon

12 sided polygon - dodecagon

13 sided polygon - tridecagon

14 sided polygon - tetra decagon

15 sided polygon - pentadecagon

and so on

20 sided polygon - icosagon

Area of an Irregular Polygon

Method 1: ( Plane figure method )

Step 1: Trace the figure on the a graph.

Step 2: Split it into plane figures which are non-overlapping.

Step 3: Find the area of each figure using appropriate formula.

Step 4: Add all the areas which will give the area of the required polygon.


Graphical method: (using co-ordinate geometry )

We follow the following steps to find the area of a polygon using graph sheet:

Step 1: Trace the given polygon on the graph sheet and mark the coordinates of each vertices.

Step 2: Draw the diagonals, such that the polygon is split into non-overlapping triangles.

[ by drawing diagonals from the same vertex ]

Step 3: Find the area of each triangle using the formula,

Area of a triangle whose vertices are, (x1 , y1 ), ( x2 , y2 ), (x3 , y3 ) is $\frac{1}{2}$[x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]

Since area can never be negative we consider the positive value of each.

Step 4: Add the areas of the triangles obtained from step 3.