Let's do this question in the figure of a regular hexagon is given angle B or C, that's this angle
over here is equal to angle Q or C, that's this angle over here is equal to 90 degrees.
So these two angles are 90 degree angles.
Find the ratio of the area of the shaded region to the unshielded region.
All right.
What's the big deal?
Give it a try and then let's do it together.
All right.
We're back.
Let's do it together.
We have seen previously how we can divide a regular hexagon.
And this is a regular hexagon right into equal areas.
But one way was like this.
Right now you can see that this area over here is what we had over here.
Right, because this angle over here is also a 90 degree angle.
Similarly, another way in which this could have been done is like this right over here.
You can see this area is something that we had over here.
So we can understand that over here, this area is one by 12 of the area of the hexagon.
Right.
Why is that?
So we have seen that in this case, we had divided the hexagon into 12 equal area parts.
Right.
And we are taking one part out of it, but that is one out of 12, hence one by 12, the area of the
hexagon.
Similarly, this is also one by 12, the area of the hexagon right here, because over here, again,
we are divided this hexagon into 12 equal parts.
And we are just taking one part over here right now.
Another way in which you can think of it is if you take this and put it over here, right.
You can put this area over here and then you would get one out of six equilateral triangles into which
you can divide the area of the hexagon.
Right.
You can imagine shifting this area to this place.
Then one particular triangle would have been shaded and then it would be taking one out of six equilateral
triangles and shading it all.
Therefore, directly, you can find out that the answer is to divide it by ten.
Right.
We are asked to find the area of the shaded region to the uncharted region.
So in this case, you we have divided into 12 equal parts.
We are taking one part and we are taking one more part.
So that's two in the numerator.
And the remaining part will be equal to ten areas.
Right.
So the ratio is 2x by 10x, which is the same as two Biton.
Now this is equal to one by five.
Now, if you think of it in this manner, one out of six equilateral triangles, then you're shading
one equilateral triangle and the remaining five equal triangles are left unchanged.
That's why the ratio is equal to one by five, which is the same as two Biton.