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.

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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 = $\left(2n-4\right)\times 90\xb0$

where each interior angle = $\frac{\left(2n-4\right)\times 90\xb0}{n}$

(ii) A regular polygon has all…

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