Let's do this question to trapezius are inscribed in a circle of diameter, 20 centimeter as shown in
the figure, find the shaded area.
All right, pause the video, give it a try, and then let's do it together.
All right.
We are back.
Let's do it together.
You can see over here that this side is equal to this side and that's equal to the side right now.
Over here, the case is the same.
The side, the site and this side.
These three sides are equal.
Right.
And it's inscribed in this circle.
Now you can see that it's forming a regular hexagon, right?
All these six sides are equal.
And over here you have the diameter of the circle.
Now, let's join this point.
That is the center of the circle to these vertices over here.
All right.
Now, over here you have one, Topsham.
And if I join these, what takes us to the midpoint, I get this over here, this divides the tropism
over here into three equilateral triangles right now.
Let me find the area of this regular hexagon that would be six times the area of one of the equilateral
triangles, right.
But that's Route three by four into a square.
Over here, it's given that the diameter is 20 centimeter.
Therefore, the side of this regular hexagon is equal to 10 centimeters.
Right.
This is equal to 20.
So this much over here will be 10 centimeter.
All right, so this is the area of this ship that is the regular hexagon, so that simplifies to 150
route, three centimeter square.
Now, we have seen how we can divide this into equal parts farther.
Right.
Let me draw these lines.
I have one line over here, one over here and one over here.
In this manner, we have divided this tropism into six equal parts.
Right to one tropism is divided into six equal parts.
If I do the same thing for the tropism below to trapezius would be divided into 12 equal parts to Trapezius
or the regular hexagon we have seen before.
All we can divide the regular hexagon into 12 equal parts.
Right.
You just need to extend these lines to this part as well.
All right.
Now, the question says that find the shaded area.
So you just need to find this.
Plus this, plus this.
Plus this.
So how many of the 12 equal parts do you need to take out so that you get what is asked in the question?
You just need to take out these four parts, right.
Or take out these four parts out of this part.
Right.
This area.
So for that, you need to divide this area divided into 12 equal parts.
And take out four parts to the answer would be or divided by 12 into 150 root three, and that is equal
to 50 root three centimeter square.
And that is your answer.