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Polygons

Polygons and their Attributes

Let us consider a square and a rhombus.

What is the difference between the two figures?

We can see that in a square, all the sides are equal and all the angles are also of equal measure. On the other hand, in a rhombus, all sides are equal; however, the measures of all angles are not equal.

We thus say that a square is a regular polygon and a rhombus is an irregular polygon.

The regular and irregular polygons can be defined as follows.

 “Polygons in which all sides are of equal length and all interior angles of equal measure are known as regular polygons”.
 “Polygons in which all sides are not of equal length and all angles are not of equal measure are known as irregular polygons”.

Let us see another example.

A regular hexagon has all sides of equal length. Moreover, all the angles are of equal measure 120°.

However, in case of an irregular hexagon, all the sides are not of equal length. Also, all the angles are not equal. A regular and an irregular hexagon are shown in the following figure.

Formulas Related to Regular Polygons:

(i) The sum of the interior angles of an n sided polygon = $\left(2n-4\right)×90°$

where each interior angle = $\frac{\left(2n-4\right)×90°}{n}$

(ii) A regular polygon has all…

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