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In this video, let's play around a little bit more about inscribing a circle in a square.

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Now, over here we have this shape and we have discussed how to find this area right now.

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Imagine you are asked to find this area.

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How would you approach it?

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Let's just think about it.

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All right.

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So this is the area that we are trying to find out.

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Now, let me join these points together and these points together so it would look like this right now

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over here, this area over here.

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Right.

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That is the same as this spot over here.

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Right.

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All right, so let's think about it a little bit more, why it is the same, let me take this part out.

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OK, now let me rotate it and let me keep it back.

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OK, so you can see that over here, this area is the same as this area over here.

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Right?

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So that's why these two are equal.

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And this is what we had over here also.

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All right.

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Now, imagine that you want to find this area, can you tell me how that can be done?

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Imagine this is four centimeter.

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All right, then the area of the square would be 16 centimeters square right now.

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Over here, the area of the circle would be by in dofor.

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Right.

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Why is that?

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So it's Pyar Square.

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The radius would be too.

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Right, because the site is for all right now.

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What would be this area over here?

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That area would be 16, which is the squares area minus four percent.

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That's the circle area divided by four.

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Right.

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But this area over here will be 16 minus four.

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Buy into one by four.

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Right now, can you tell me how we can find this area over here?

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This would be nothing but finding this area.

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And then you need to subtract two times this area because we have seen that this and this is equal.

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Right.

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So this area over here will be this much, which is one by four out of 16.

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Right.

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Because this is obtained when you divide the square into four equal parts with this match over here

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is 16 by four, which is equal to four.

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So to get this shaded part, you need to do four minus two times, one by four out of sixteen minus

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four point, which is this part over here.

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Right.

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And this simplifies to four minus two in the four minus five, which is equal to two by minus four.

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So that would be this shaded part over here.