Polygon forms an essential part of Quant section in CAT, XAT and other MBA entrance tests. It can be the easiest topics of Quantitative Aptitude, if you prepare it well. In this blog we are going to discuss some basic properties of polygons with more than 4 sides.

**Classification of Polygons **:

**Simple** **Polygon** – It has only one boundary, and it doesn’t cross over itself.

**Complex** **Polygon** – This polygon intersects itself! Many rules about polygons don’t work when it is complex. However, for CAT Exam syllabus is limited to only simple polygons.

**Convex Polygon** – In this polygon, no internal angle can be more than 180°. This polygon has no angles pointing inwards.

**Concave Polygon** – A polygon in which at least one of the interior angles is more than 180° is called a concave polygon.

**Regular Polygon** – A polygon in which all the sides are equal and all the angles are equal.

**Irregular Polygon** – A polygon where all the sides and angles are not equal.

### *All regular polygons are convex polygons.

**Area of Regular Polygon **:

**Area of any regular polygon can be given by :** $latex \displaystyle \frac{1}{2}\text{ }N\text{ Sin(}\frac{{{{{360}}^{o}}}}{N}\text{)}{{\text{S}}^{2}}$

where ‘N’ is number of sides and ‘S’ is the length of one side.

**Interior Angles :**

- Sum of all the interior angles of a convex or concave polygon : $latex \displaystyle {{180}^{o}}\text{ (N – 2)}$
- Measure of each interior angles of a regular polygon : $latex \displaystyle \frac{{\text{(N – 2) }{{{180}}^{o}}}}{\text{N}}$

**Exterior Angles :**

- Sum of all the exterior angle of a convex or concave polygon is always 360 degrees.
- Measure of each exterior angle of a regular polygon = $latex \displaystyle \frac{{{{{360}}^{o}}}}{N}$

**Diagonals : **

Number of Diagonals in a Polygon : $latex \displaystyle \frac{{n(n-3)}}{2}$

**An interesting Example **:

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