High students in this video, let's discuss an important method that will help us solve a lot of geometry
questions in a very quick manner that's called graphical division.
First, I will tell you what we mean with this.
And let me take an example to convince you of the benefits of this method.
All right.
Let's get started.
What is graphical division?
It involves dividing a given figure into equal areas, such that points which are part of the question
are also part of the division.
All right.
What do I mean with this?
Let's try to understand this with an example.
Over here you have a square.
And let's say that the area of the square, ABCDE is given a 20 centimetre square.
Now, I will take a very simple example just to convince you of the benefits of this method.
Then we will see more difficult questions.
All right.
Now, see this point over here and this point over here are midpoints of A, B and C, let's call them
as F and eat.
So F is the midpoint of AB and is the midpoint of DC and say you are given a question that asks you
to find this shaded region.
All right.
There can be two approaches with which you can find this approach.
One would be you find that the length of a B right is square root of twenty because it's given that
the area of the square is 20 centimetres square.
We know that area of square is side square.
Therefore, a B can be found as root of twenty, which is 2.5.
After that you find F be, you know, F is the midpoint of A B, therefore if B will be off of B that
is root of five.
Now if it is equal to A B, right.
Because if he is equal to 80, which is equal to a B, so I have F is equal to 2.5.
And after finding these sites now I have a rectangle over here.
Therefore I can find the area of FBC as root fif into two root five.
That gives me 10 centimeter square.
All right.
Now what is the other method with which we can find this answer?
We could have just done it in this manner, right?
We know that the area of the square is 20 centimetres square and we can see that if it is dividing it
into two equal parts.
Right.
Therefore, the area of this shaded region will be twenty, divided by two, which is equal to ten centimetre
square.
You can see that this method is much faster than this method in obtaining this answer.
And we guard this using the method of graphical division.
Right.
We were able to divide this area into two equal house and we knew the area of ABCDE.
Therefore the area of FBC is just half of twenty, which is equal to ten centimetres square.
Now let's see various cases such as a hexagon, a Topsham Square and equilateral triangle, etc., where
we can apply this method.