1 00:00:00,740 --> 00:00:07,580 High students so far, we have discussed about inscribing a circle in a square and doing that repeatedly 2 00:00:07,610 --> 00:00:09,020 right in this video. 3 00:00:09,170 --> 00:00:15,760 Let's talk about inscribing a circle, a hexagon and a triangle and all of these regular shapes, OK, 4 00:00:15,890 --> 00:00:19,670 a regular hexagon and a regular triangle inside a square. 5 00:00:19,940 --> 00:00:20,300 All right. 6 00:00:20,300 --> 00:00:21,480 Over here you have a square. 7 00:00:21,680 --> 00:00:22,850 Let it be of sight. 8 00:00:23,540 --> 00:00:24,120 OK. 9 00:00:24,290 --> 00:00:27,350 Now, the area of this square is equal to a square. 10 00:00:27,360 --> 00:00:28,070 We have seen that. 11 00:00:28,290 --> 00:00:28,790 All right. 12 00:00:28,980 --> 00:00:31,970 Now let me inscribe a circle inside the square. 13 00:00:32,210 --> 00:00:39,550 Now the radius of this circle will be able to write and therefore the area of the circle will be by 14 00:00:39,560 --> 00:00:41,150 by four into a square. 15 00:00:41,360 --> 00:00:42,650 And we have seen why that is. 16 00:00:42,800 --> 00:00:47,560 If you draw the diameter over here, you will see that two are is equal to it. 17 00:00:47,690 --> 00:00:50,120 And that's why we are able to. 18 00:00:50,270 --> 00:00:51,560 So we have seen this before. 19 00:00:51,860 --> 00:00:52,310 All right. 20 00:00:52,490 --> 00:00:58,440 Now, let's extend this concept to a hexagon and an equilateral triangle. 21 00:00:58,820 --> 00:00:59,230 All right. 22 00:00:59,360 --> 00:01:04,640 Now, first we inscribe a hexagon inside this circle that would look like this. 23 00:01:05,130 --> 00:01:08,050 OK, now let me make a copy of this shape over here. 24 00:01:08,270 --> 00:01:15,980 And you can see that this regular hexagon can be divided into six equilateral triangles. 25 00:01:15,980 --> 00:01:16,340 Right. 26 00:01:16,520 --> 00:01:20,510 And the side of each equilateral triangle will be equal to about two. 27 00:01:20,510 --> 00:01:20,860 Right. 28 00:01:20,960 --> 00:01:27,470 Because over here you can see that this plus this is equal to the diameter of the circle, which is 29 00:01:27,470 --> 00:01:28,540 equal to eight. 30 00:01:28,550 --> 00:01:28,880 Right. 31 00:01:28,910 --> 00:01:29,500 This is it. 32 00:01:29,660 --> 00:01:33,110 Therefore, this match over here will be equal to a by two. 33 00:01:33,260 --> 00:01:36,050 And that is the side of the hexagon. 34 00:01:36,530 --> 00:01:36,790 Right. 35 00:01:36,860 --> 00:01:38,870 So this is also equal to EBITA. 36 00:01:39,200 --> 00:01:46,970 Now, we have found that the side of the hexagon is equal to about two and hence the area of the regular 37 00:01:46,970 --> 00:01:55,220 hexagon will be six times Route three by four in the side square side is able to side squares is square 38 00:01:55,220 --> 00:01:55,820 by four. 39 00:01:56,000 --> 00:02:01,070 So six in the row, three by four in the square by four is the area of this hexagon. 40 00:02:01,250 --> 00:02:04,680 And that is equal to three room, three by eight square. 41 00:02:04,970 --> 00:02:05,450 All right. 42 00:02:05,630 --> 00:02:11,500 Now let's proceed and create a regular triangle inside the hexagon. 43 00:02:11,510 --> 00:02:15,740 And remember, a regular triangle is an equilateral triangle. 44 00:02:16,010 --> 00:02:16,450 All right. 45 00:02:16,580 --> 00:02:19,350 So that would look like this now over here. 46 00:02:19,520 --> 00:02:23,180 Let's see how to find the length of the side of the triangle. 47 00:02:23,390 --> 00:02:25,700 Over here, I have this equilateral triangle. 48 00:02:25,790 --> 00:02:27,800 Right, which is part of the regular hexagon. 49 00:02:28,040 --> 00:02:33,620 Now, if I drop a perpendicular from this vertex to this site, that would look like this right now, 50 00:02:33,620 --> 00:02:36,190 what would be the length of this height? 51 00:02:36,860 --> 00:02:41,990 We know that the height of an equilateral triangle is Route three by two into the side. 52 00:02:42,170 --> 00:02:48,730 Right now we have found the side of this equilateral triangle as EBITA two, because that's all we found. 53 00:02:48,750 --> 00:02:55,880 The side of the hexagon is able to rule three by two in the side is equal to room three by two into 54 00:02:55,880 --> 00:02:56,600 a by two. 55 00:02:56,720 --> 00:02:57,110 Right. 56 00:02:57,950 --> 00:02:58,410 All right. 57 00:02:58,550 --> 00:03:01,130 Now, this is the height of the equilateral triangle. 58 00:03:01,280 --> 00:03:04,120 Now this is a three by two in the air by two. 59 00:03:04,370 --> 00:03:07,250 That gives you room three by four into it. 60 00:03:07,520 --> 00:03:10,490 So that is half of the side of the equilateral triangle. 61 00:03:10,670 --> 00:03:11,050 Right. 62 00:03:11,230 --> 00:03:18,920 Therefore, the side of the triangle will be two times Route three by four into a that's equal to room 63 00:03:18,920 --> 00:03:20,790 three by two into it. 64 00:03:20,990 --> 00:03:23,090 So that is the site of the equilateral triangle. 65 00:03:23,330 --> 00:03:26,630 Now we know how to find the area of triangle. 66 00:03:26,810 --> 00:03:29,760 That would be Route three by four sides square. 67 00:03:29,930 --> 00:03:30,340 Right. 68 00:03:30,500 --> 00:03:35,210 And that is equal to room three by four into room three by two. 69 00:03:35,230 --> 00:03:37,580 Eight that is this the whole square. 70 00:03:38,650 --> 00:03:42,700 Right, that simplifies to three through three by 16 is square. 71 00:03:42,910 --> 00:03:45,900 Now, you don't need to buy any of these formulas. 72 00:03:46,120 --> 00:03:51,760 All you need to know is this approach, because if you needed for a question, if you know this approach, 73 00:03:51,850 --> 00:03:57,190 you can easily derive whatever you need and find the answer and get out of the question. 74 00:03:57,520 --> 00:03:58,660 All right, now. 75 00:03:59,790 --> 00:04:03,450 Let's also analyze the parameters of these shapes. 76 00:04:03,690 --> 00:04:06,750 OK, so what is the perimeter of the square over here? 77 00:04:06,960 --> 00:04:11,020 It's offsite, hence the perimeter is for it right now. 78 00:04:11,040 --> 00:04:12,460 What about the circle? 79 00:04:12,630 --> 00:04:18,720 We have found that the radius of the circle is about to therefore the circumference of the circle will 80 00:04:18,720 --> 00:04:23,190 be to pay into a bitou that's equal to buy into it. 81 00:04:23,460 --> 00:04:24,680 What about the hexagon? 82 00:04:24,810 --> 00:04:31,020 We have found the site is able to therefore the perimeter of the hexagon will be six a by two. 83 00:04:31,230 --> 00:04:33,210 That's equal to three, right? 84 00:04:33,230 --> 00:04:34,120 This is three eight. 85 00:04:34,380 --> 00:04:36,180 And what about the triangle? 86 00:04:36,390 --> 00:04:38,790 We know that the site is Route three by two. 87 00:04:39,210 --> 00:04:44,700 Therefore, the perimeter of the triangle will be three in the three by two a.