1 00:00:00,620 --> 00:00:07,790 High students in this video, let's discuss an important method that will help us solve a lot of geometry 2 00:00:07,790 --> 00:00:12,020 questions in a very quick manner that's called graphical division. 3 00:00:12,290 --> 00:00:14,870 First, I will tell you what we mean with this. 4 00:00:15,050 --> 00:00:20,780 And let me take an example to convince you of the benefits of this method. 5 00:00:20,960 --> 00:00:21,410 All right. 6 00:00:21,410 --> 00:00:22,340 Let's get started. 7 00:00:22,550 --> 00:00:23,960 What is graphical division? 8 00:00:24,260 --> 00:00:32,630 It involves dividing a given figure into equal areas, such that points which are part of the question 9 00:00:32,630 --> 00:00:34,610 are also part of the division. 10 00:00:34,880 --> 00:00:35,320 All right. 11 00:00:35,480 --> 00:00:36,730 What do I mean with this? 12 00:00:36,740 --> 00:00:39,360 Let's try to understand this with an example. 13 00:00:39,710 --> 00:00:41,900 Over here you have a square. 14 00:00:42,230 --> 00:00:49,550 And let's say that the area of the square, ABCDE is given a 20 centimetre square. 15 00:00:49,730 --> 00:00:55,510 Now, I will take a very simple example just to convince you of the benefits of this method. 16 00:00:55,700 --> 00:00:57,890 Then we will see more difficult questions. 17 00:00:58,190 --> 00:00:58,590 All right. 18 00:00:58,760 --> 00:01:06,560 Now, see this point over here and this point over here are midpoints of A, B and C, let's call them 19 00:01:06,560 --> 00:01:08,240 as F and eat. 20 00:01:08,450 --> 00:01:15,290 So F is the midpoint of AB and is the midpoint of DC and say you are given a question that asks you 21 00:01:15,290 --> 00:01:17,420 to find this shaded region. 22 00:01:17,690 --> 00:01:18,100 All right. 23 00:01:18,320 --> 00:01:22,080 There can be two approaches with which you can find this approach. 24 00:01:22,100 --> 00:01:30,200 One would be you find that the length of a B right is square root of twenty because it's given that 25 00:01:30,200 --> 00:01:32,910 the area of the square is 20 centimetres square. 26 00:01:33,200 --> 00:01:35,590 We know that area of square is side square. 27 00:01:35,840 --> 00:01:40,500 Therefore, a B can be found as root of twenty, which is 2.5. 28 00:01:40,730 --> 00:01:48,710 After that you find F be, you know, F is the midpoint of A B, therefore if B will be off of B that 29 00:01:48,710 --> 00:01:49,680 is root of five. 30 00:01:49,910 --> 00:01:52,750 Now if it is equal to A B, right. 31 00:01:52,940 --> 00:01:59,110 Because if he is equal to 80, which is equal to a B, so I have F is equal to 2.5. 32 00:01:59,390 --> 00:02:03,350 And after finding these sites now I have a rectangle over here. 33 00:02:03,530 --> 00:02:09,620 Therefore I can find the area of FBC as root fif into two root five. 34 00:02:09,860 --> 00:02:11,870 That gives me 10 centimeter square. 35 00:02:12,170 --> 00:02:12,640 All right. 36 00:02:12,890 --> 00:02:16,560 Now what is the other method with which we can find this answer? 37 00:02:16,830 --> 00:02:18,930 We could have just done it in this manner, right? 38 00:02:19,160 --> 00:02:27,020 We know that the area of the square is 20 centimetres square and we can see that if it is dividing it 39 00:02:27,020 --> 00:02:28,400 into two equal parts. 40 00:02:28,400 --> 00:02:28,740 Right. 41 00:02:28,940 --> 00:02:34,580 Therefore, the area of this shaded region will be twenty, divided by two, which is equal to ten centimetre 42 00:02:34,580 --> 00:02:35,080 square. 43 00:02:35,330 --> 00:02:41,570 You can see that this method is much faster than this method in obtaining this answer. 44 00:02:41,720 --> 00:02:45,200 And we guard this using the method of graphical division. 45 00:02:45,200 --> 00:02:45,510 Right. 46 00:02:45,770 --> 00:02:51,690 We were able to divide this area into two equal house and we knew the area of ABCDE. 47 00:02:51,920 --> 00:02:58,610 Therefore the area of FBC is just half of twenty, which is equal to ten centimetres square. 48 00:02:58,850 --> 00:03:06,410 Now let's see various cases such as a hexagon, a Topsham Square and equilateral triangle, etc., where 49 00:03:06,410 --> 00:03:08,300 we can apply this method.