Sum of the interior angles of the Polygon

Find the sum of the angles of the polygon

Solution :: First we find the Sum of the interior angles of the triangle and we relate it further to the polygons with 4,5,6 sides and so on...

For a quadrilateral : Number of triangles possible are 2,
For a pentagon.     :  Number of triangles possible are 3,
For a hexagon.       : Number of triangles possible are 4,

For a n- sided polygon number of triangles possible are (n-2)

The sum of the interior angles of a n-sided polygon are (n-2)*180° = (n-2)*π radians.

Areas Applications

Find the area of the figures from the geometry you know so far.

Solution :: The given figures are 1. Regular Hexagon, 2. Regular Pentagon 3. Area of the shaded part   4. Area of the shaded part

Area of Triangle applications

Some figures are given. Find the areas of them using the geometry known to you so far.
Using area of triangle

Solution :: The area of the figures can be found

Pascal Triangle

Do you know what is a Pascal triangle and what is its use?

Solution :: A Pascal triangle is used to calculate the binomial coefficients without much
                   struggle. The triangle is drawn as follows.
                   Start with 1 (This is the first row element,which can be said as 0! )
                    Now the second row can be obtained by adding the two elements of the first row
                     (i.e., 1 and 1)
                    The third row is obtained by writing the end terms as 1 and the remaining by
                     adding the terms in the previous row and which are present above it.
                     The subsequent rows can be obtained in the same manner...
                                                                    1
                                                                1 -    1
                                                           1 -    2 -    1
                                                       1 -  3 -     3 -    1
                                                         (1+2)   (2+1)
                                                   1 -   4 -     6 -     4 -   1
                                                     (1+3)  (3+3) ( 3+1)
                                              1 -    5 -     10 -    10 -   5 -   1
                                                   (1+4) (4+6) (6+4) (4+1)
                                        1  -   6  -   15  -    20  -    15   -    6 -   1
                               
                                   1 -    7 -   21 -    35 -   35 -     21 -    7 -   1

                               1 -     8 -   28 -   56 -   70 -    56 -    28 -   8 -     1

Length of Altitude in a right angled triangle

Find the length of the altitude of a right angled triangle where the sides are given by 'a' and 'b'.

Solution:: There are many ways to solve this problem....
Method :1 Similar Triangles Concept

Method 2 :: Trigonometric Approach

Method 3 :: Pythagoras Theorem

Method 4 :: Straight Lines Approach

Method 5 ::  Area of Triangle Approach

Division of a Circle

Divide a circle into 'n' parts and what is the geometry of each part?

Solution:: Suppose if a line is drawn through the centre of a circle then it will divide it into 2 equal parts and if you draw 2 lines at right angles passing through the centre then it will divide into 4 equal parts...and for 3 lines at 60° each then 6 parts and it goes on...

For odd number of parts what we have to do??

It's simple as it sounds because initially we used angle concept.. The same can be applied here also.. If we want 3 equal parts then the angle at the centre should be divided by 3 , for 5 parts the angle at the centre is divided by 5 and so on..

If you want to divide into 'n' parts then the angle at the centre is divided by 'n'.
The angle of each part is (360/n)° and all the parts are sectors with equal area.

Let's see this diagrammatically...