Let's do this question and Sakalys inscribed in a square ABCDE inside the circle, another square BQ
office is inscribed.
The diameter of the circle is six centimeter.
Find the shaded area.
All right, pause the video, give it a try, and then let's do it together.
All right.
Let's get started.
So we have a shaded part over here and a shaded part over here.
So let me call this one and let me call this, too.
Now, let's find one first.
Now, one would be one by fort.
The difference of the area of this square and this circle.
Is that true?
Right.
That's true.
Right.
If I subtract the area of the square minus the area of the circle, I'll get this.
Plus this, plus this, plus this.
Right.
And I just need this.
So I need to take one by fort, the different of the area of the square and the circle.
All right.
Now, over here you can see that the diameter of the circle is equal to the side of the square, right.
To draw the diameter like this, you can see that that's equal to eight.
Right.
So the diameter of the circle is equal to the side of ABCDE.
Therefore, I know that the area of ABCDE is six to six right over here.
This is given a six.
So this is also equal to six.
So area of ABCDE will be six in the six and over here as their diameter is six, the radius will be
three.
Therefore the area of the circle is bindu three square.
So this is one by four to six square minus by into three square.
That gives you this shaded region.
Right.
And this is equal to thirty six minus nine pi divided by four.
All right, let's find the second part.
This would be one by fourth, the area of the circle minus the area of the square.
Right.
Because if you subtract the area of the circle and then minus the area of the square, you'll get this
plus this, plus this, plus this.
Right.
And you just need this.
So you need to take one by fourth.
So this over here will be one by fourth area of the circle, minus area of BQ.
Q Right.
And over here we know that the area of the circle is nine five and the area of P you are, as we have
seen, will be half of the area of ABCDE.
Right.
So that would be half of area of a city.
That's half of 36.
Right.
So this becomes one by fort of nine by minus 18.
All right.
So now we have this and this.
Now the answer would be this plus this, right?
Because we need this and this together.
So one and two together gives one by four out of thirty six minus nine by plus nine by minus 18.
And that is equal to.
Eighteen by four or nine by two centimeter square.
And that is a solution to this question.
Now let's see one more approach in which this could have been done over here.
You can see that this distance is half of it.
That's Aebi, too, right?
Similarly, this is also half of.
So this is also able to right this part over here.
If you join this together, this would be of length route to into EBITA or Ebeye.
Route to.
Right.
Therefore, you can see that you can actually rotate this square over here and it will look like this.
Right.
The site of this square also is a by route to.
Right.
And that's why the area of the square we saw is half the area of the outer square because the area is
able to do able to that's equal to a square by two.
That is half of the area of the outer square.
But this site also is able to and we have seen this is also able to so you can actually rotated and
then it look like this.
Now you just need to take one by fourth of the difference of the area of ABCDE and Bhiku Orris, this
one over here.
Right.
Why is that?
So if you subtract the area of ABCDE and then from that you subtract this part, you are left with this,
plus this, plus this, plus this.
And this is one bifold of that.
Right.
All right.
Let me make some space over here.
So that is equal to one by fourth of half of the area of ABCDE.
Why is that so?
Because the area we saw of Piku Outis is half the area of ABCDE.
So if you subtract area of ABCDE.
Minus area of BQ Orris.
You can write this as area of ABCDE.
Minus area of ebiquity by two, right, because we have seen that area of procuracy will be half the
area of ABCDE, when you do this subtraction, you get area of ABCDE by two and you need to take one
by fourth of that because you just need that.
All right.
So this area over here is equal to six into six.
So that's six.
The six by two into one by four.
Right.
And what is the answer that you get that is equal to.
Nine by two, right, one by four into one by two in the six in the six.
That gives you nine by two centimeter square.
And that is the same answer that we got before.