1
00:00:00,650 --> 00:00:08,270
Let's do this question in the figure of a regular hexagon is given angle B or C, that's this angle

2
00:00:08,270 --> 00:00:14,330
over here is equal to angle Q or C, that's this angle over here is equal to 90 degrees.

3
00:00:14,660 --> 00:00:16,840
So these two angles are 90 degree angles.

4
00:00:17,150 --> 00:00:21,710
Find the ratio of the area of the shaded region to the unshielded region.

5
00:00:22,010 --> 00:00:22,490
All right.

6
00:00:22,790 --> 00:00:23,630
What's the big deal?

7
00:00:23,750 --> 00:00:26,030
Give it a try and then let's do it together.

8
00:00:26,630 --> 00:00:27,080
All right.

9
00:00:27,080 --> 00:00:27,660
We're back.

10
00:00:27,680 --> 00:00:28,710
Let's do it together.

11
00:00:29,000 --> 00:00:33,140
We have seen previously how we can divide a regular hexagon.

12
00:00:33,320 --> 00:00:36,650
And this is a regular hexagon right into equal areas.

13
00:00:36,930 --> 00:00:38,750
But one way was like this.

14
00:00:38,760 --> 00:00:43,600
Right now you can see that this area over here is what we had over here.

15
00:00:43,600 --> 00:00:47,120
Right, because this angle over here is also a 90 degree angle.

16
00:00:47,390 --> 00:00:52,370
Similarly, another way in which this could have been done is like this right over here.

17
00:00:52,370 --> 00:00:56,120
You can see this area is something that we had over here.

18
00:00:56,480 --> 00:01:04,110
So we can understand that over here, this area is one by 12 of the area of the hexagon.

19
00:01:04,130 --> 00:01:04,380
Right.

20
00:01:04,580 --> 00:01:05,120
Why is that?

21
00:01:05,120 --> 00:01:12,860
So we have seen that in this case, we had divided the hexagon into 12 equal area parts.

22
00:01:12,860 --> 00:01:13,180
Right.

23
00:01:13,190 --> 00:01:18,980
And we are taking one part out of it, but that is one out of 12, hence one by 12, the area of the

24
00:01:18,980 --> 00:01:19,520
hexagon.

25
00:01:19,760 --> 00:01:26,210
Similarly, this is also one by 12, the area of the hexagon right here, because over here, again,

26
00:01:26,210 --> 00:01:29,510
we are divided this hexagon into 12 equal parts.

27
00:01:29,690 --> 00:01:33,020
And we are just taking one part over here right now.

28
00:01:33,530 --> 00:01:38,690
Another way in which you can think of it is if you take this and put it over here, right.

29
00:01:39,080 --> 00:01:45,800
You can put this area over here and then you would get one out of six equilateral triangles into which

30
00:01:45,800 --> 00:01:48,280
you can divide the area of the hexagon.

31
00:01:48,290 --> 00:01:48,570
Right.

32
00:01:48,770 --> 00:01:51,290
You can imagine shifting this area to this place.

33
00:01:51,560 --> 00:01:58,340
Then one particular triangle would have been shaded and then it would be taking one out of six equilateral

34
00:01:58,340 --> 00:02:00,200
triangles and shading it all.

35
00:02:00,620 --> 00:02:05,370
Therefore, directly, you can find out that the answer is to divide it by ten.

36
00:02:05,560 --> 00:02:05,780
Right.

37
00:02:06,030 --> 00:02:10,340
We are asked to find the area of the shaded region to the uncharted region.

38
00:02:10,520 --> 00:02:14,300
So in this case, you we have divided into 12 equal parts.

39
00:02:14,480 --> 00:02:17,170
We are taking one part and we are taking one more part.

40
00:02:17,390 --> 00:02:19,100
So that's two in the numerator.

41
00:02:19,250 --> 00:02:23,000
And the remaining part will be equal to ten areas.

42
00:02:23,000 --> 00:02:23,310
Right.

43
00:02:23,510 --> 00:02:27,780
So the ratio is 2x by 10x, which is the same as two Biton.

44
00:02:28,070 --> 00:02:30,770
Now this is equal to one by five.

45
00:02:30,980 --> 00:02:36,290
Now, if you think of it in this manner, one out of six equilateral triangles, then you're shading

46
00:02:36,290 --> 00:02:40,930
one equilateral triangle and the remaining five equal triangles are left unchanged.

47
00:02:41,000 --> 00:02:46,580
That's why the ratio is equal to one by five, which is the same as two Biton.