Students in this video, let's discuss how we can divide an equilateral triangle into equal area shapes.
All right, now over here, if I join the midpoints of these three sites, right, you can see that
I will get four congruent triangles.
These are of equal area.
So if I just take one out of them, it will be one by fourth the area of this equilateral triangle.
Now, let me take one more copy of the Golden Triangle over here.
Now I can divide it into more number of equal parts in this manner.
So over here, you can see that these two points dissect the site over here now in this way, you have
divided this equilateral triangle into nine equal parts.
All right.
Now let's proceed and see how we can divide a square into equal parts.
See, over here, we are all taking regular shapes.
We took a regular hexagon and equilateral triangle and a square, all of these are regular shapes and
we took an isosceles prop. where the nonpareil side was equal to this smaller parallel side.
All right.
Now let's proceed.
Over here, we have a square I can divide a square in two or equal parts in this manner.
So these areas will be equal or I can divide it like this into four equal parts or square can be divided
like this into four equal parts.
Now, over here, when you do this, these lengths have to be equal.
Right.
So if the site of this square is a, then X over here has to be divided by four.
Now, I can divide a square like this also.
Right.
That's obtained by taking it like this.
And then you draw a line like this.
Right.
This line splits this smaller square into two halves, evenly split this one into two halves.
And you draw a line like this and this one will split these two into equal halves and these two into
equal halves.
So you get one, two, three, four, five, six, seven, eight.
So in this way, you get eight equal parts.
Right.
And you can do it like this also.
Right.
But this is also one, two, three, four, five, six, seven, eight.
But these are also eight equal parts of the square.
Let's see some more ways in which a square can be divided, you can divide it like this.
This would be six equal parts, right?
This would be three equal parts.
This would be nine equal parts.
Right.
What about this?
This is one, two, three, four, five, six, six equal parts.
Right.
And over here, if you do this, then this has to be equal to this and it has to be equal to this.
So this point and this point bisects this site.
And this is also a way in which you can divide the square into a larger number of equal parts.
So you can see that it's one, two, three, four, five, six, seven, eight, nine, 10, 11, 12,
12.
In the two, that's twenty four equal parts over here.
It'll depend upon the question.
Remember, the definition of graphical division is you take or you create a division such that points
mentioned in the question are part of the graphical division.
So the way in which you divide the square will depend upon the question which you are trying to address.