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Students in this video, let's discuss how we can divide an equilateral triangle into equal area shapes.

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All right, now over here, if I join the midpoints of these three sites, right, you can see that

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I will get four congruent triangles.

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These are of equal area.

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So if I just take one out of them, it will be one by fourth the area of this equilateral triangle.

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Now, let me take one more copy of the Golden Triangle over here.

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Now I can divide it into more number of equal parts in this manner.

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So over here, you can see that these two points dissect the site over here now in this way, you have

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divided this equilateral triangle into nine equal parts.

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All right.

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Now let's proceed and see how we can divide a square into equal parts.

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See, over here, we are all taking regular shapes.

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We took a regular hexagon and equilateral triangle and a square, all of these are regular shapes and

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we took an isosceles prop. where the nonpareil side was equal to this smaller parallel side.

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All right.

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Now let's proceed.

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Over here, we have a square I can divide a square in two or equal parts in this manner.

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So these areas will be equal or I can divide it like this into four equal parts or square can be divided

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like this into four equal parts.

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Now, over here, when you do this, these lengths have to be equal.

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Right.

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So if the site of this square is a, then X over here has to be divided by four.

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Now, I can divide a square like this also.

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Right.

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That's obtained by taking it like this.

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And then you draw a line like this.

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Right.

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This line splits this smaller square into two halves, evenly split this one into two halves.

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And you draw a line like this and this one will split these two into equal halves and these two into

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equal halves.

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So you get one, two, three, four, five, six, seven, eight.

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So in this way, you get eight equal parts.

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Right.

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And you can do it like this also.

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Right.

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But this is also one, two, three, four, five, six, seven, eight.

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But these are also eight equal parts of the square.

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Let's see some more ways in which a square can be divided, you can divide it like this.

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This would be six equal parts, right?

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This would be three equal parts.

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This would be nine equal parts.

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Right.

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What about this?

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This is one, two, three, four, five, six, six equal parts.

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Right.

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And over here, if you do this, then this has to be equal to this and it has to be equal to this.

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So this point and this point bisects this site.

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And this is also a way in which you can divide the square into a larger number of equal parts.

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So you can see that it's one, two, three, four, five, six, seven, eight, nine, 10, 11, 12,

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12.

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In the two, that's twenty four equal parts over here.

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It'll depend upon the question.

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Remember, the definition of graphical division is you take or you create a division such that points

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mentioned in the question are part of the graphical division.

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So the way in which you divide the square will depend upon the question which you are trying to address.