Polygon Concepts for CAT Exam Preparation


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.

Polygons Geometry concepts and tricks for online CAT exam preparation

 

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.

Polygons Geometry concepts and tricks for online CAT exam preparation

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 :

  1. Sum of all the interior angles of a convex or concave polygon : $latex \displaystyle {{180}^{o}}\text{ (N – 2)}$
  2. Measure of each interior angles of a regular polygon : $latex \displaystyle \frac{{\text{(N – 2) }{{{180}}^{o}}}}{\text{N}}$
Polygons Geometry concepts and tricks for online CAT exam preparation
Polygons Geometry concepts and tricks for online CAT exam preparation

 

Exterior Angles :

  1. Sum of all the exterior angle of a convex or concave polygon is always 360 degrees.
  2. Measure of each exterior angle of a regular polygon = $latex \displaystyle \frac{{{{{360}}^{o}}}}{N}$
Polygons Geometry concepts and tricks for online CAT exam preparation

 

Diagonals :

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

Polygons Geometry concepts and tricks for online CAT exam preparation
Polygons Geometry concepts and tricks for online CAT exam preparation

An interesting Example :

Polygons Geometry concepts and tricks for online CAT exam preparation
Polygons Geometry concepts and tricks for online CAT exam preparation

Do check out our other blogs to learn more concepts for CAT Exam.

You can also visit our website for free video lectures, mock tests, sectional tests and much more.

Also, visit our YouTube channel where we have discussed various tricks and tips to solve Geometry Questions easily.

 

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