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

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.

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

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, (x_{1} , y_{1} ), ( x_{2} , y_{2} ), (x_{3} , y_{3} ) is $\frac{1}{2}$[x_{1}(y_{2}-y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2})]

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.