Polygons

Hello Friends, Today i am posting few very easy formulas and tips to solve question related with polygons.

First let me tell you the meaning of polygon- Polygon is a plane figure which is started from a particular point after drawing any shape by the lines, ends on the same point.Friends it's not a definition of polygon - i just explained it so you can understand.

Its means as we are learned about triangle,rectangle,square etc in our school days, All these are polygons.

Polygons can be divided into two parts:-
1.) Polygon:-This can be again divided into two parts-

      a.)Convex :- If all the external angles are Greater than 180º.
      b.)Concave:- If any one or all angles are less than 180º.

2.)Regular Polygon:- If sides and internal angles are same it is called regular polygon.

Why polygons are used 

We normally leanr formulas to find its area with 3 sides or 4 sides but it is not necessary that a shape can be formed only with 3 or 4 sides, it can has more sides like 5,6,7,8 etc. So than we use these formulas to find it's area and all.


Few Important Notes regarding Polygons:-

1.)Some of all external angles of polygon is 360º:- Yes friends it means the sum of all external angles will be 360º ,It doesn't matter that how many sides it has.

2.)Sum of all internal angles of a polygon with 'n' sides is (n-2)*180º ,here (*=multiply)

Example:

Question:What is the sum of all the angles of a rectangular polygon?
Solution:

Friends as we have learned the sum of all the angles of a rectangle is 360º so now we will check that this formula can calculate or not

So there are 4 sides in a rectangle, Means the value of 'n' is 4

(4-2)*180
=2*180
=360    (hence proved)



3.)No. of Diagonals:-

n(n-3)/2 

Example :

How many diagonals  can be formed in a rectangle?

Solution

Friends as we know only 2 diagonals can be formed in a rectangle So let's check through the formula-

Same here n= 4

So, 4(4-3)/2

=4*1/2

=2     (hence proved)

 

# Regular Polygon:-

1.)Each interior angle of a regular polygon is 

(n-2)180/n

2.)Each exterior angle of a regular polygon is

360/n

 

3.)Area of regular polygon with 'n' sides of dimension 'S'.

n/4*S^2*Cotπ/n

{In this formula the no of sides will be divided by 4 and than multiply with the square of dimensions and than again multiply with the cot with angle (it will be taken as 180º) will be divided by the no. of sides.  }    [^= Power and *= multiply ]

Names of Polygons:-

Which has 5 Sides- Pentagon
Which has 6 Sides - Hexagon
Which has 7 Sides - Heptagon
Which has 8 Sides- Octagon
Which has 9 Sides - Nonagon
Which has 10 Sides - Decagon


Question:- Find the area of Hexagon with side of length 3m.
Answer:-
n/4*S^2*Cotπ/n

6/4*3*3*Cot 180/6

27/2*1/3*Cot 30

9√3/2

Friends this was the simple concept of polygon, by these formulas you can solve all problems asked in your exams related with polygon.

And as always don't forget to comment your Doubt and suggestion's.

Thank you☻