In this video, let's play around a little bit more about inscribing a circle in a square.
Now, over here we have this shape and we have discussed how to find this area right now.
Imagine you are asked to find this area.
How would you approach it?
Let's just think about it.
All right.
So this is the area that we are trying to find out.
Now, let me join these points together and these points together so it would look like this right now
over here, this area over here.
Right.
That is the same as this spot over here.
Right.
All right, so let's think about it a little bit more, why it is the same, let me take this part out.
OK, now let me rotate it and let me keep it back.
OK, so you can see that over here, this area is the same as this area over here.
Right?
So that's why these two are equal.
And this is what we had over here also.
All right.
Now, imagine that you want to find this area, can you tell me how that can be done?
Imagine this is four centimeter.
All right, then the area of the square would be 16 centimeters square right now.
Over here, the area of the circle would be by in dofor.
Right.
Why is that?
So it's Pyar Square.
The radius would be too.
Right, because the site is for all right now.
What would be this area over here?
That area would be 16, which is the squares area minus four percent.
That's the circle area divided by four.
Right.
But this area over here will be 16 minus four.
Buy into one by four.
Right now, can you tell me how we can find this area over here?
This would be nothing but finding this area.
And then you need to subtract two times this area because we have seen that this and this is equal.
Right.
So this area over here will be this much, which is one by four out of 16.
Right.
Because this is obtained when you divide the square into four equal parts with this match over here
is 16 by four, which is equal to four.
So to get this shaded part, you need to do four minus two times, one by four out of sixteen minus
four point, which is this part over here.
Right.
And this simplifies to four minus two in the four minus five, which is equal to two by minus four.
So that would be this shaded part over here.