# Irregular Polygon

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

## 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.

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 4 Square 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 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.