1 00:00:00,700 --> 00:00:08,590 Let's do this question to trapezius are inscribed in a circle of diameter, 20 centimeter as shown in 2 00:00:08,590 --> 00:00:11,180 the figure, find the shaded area. 3 00:00:11,590 --> 00:00:15,860 All right, pause the video, give it a try, and then let's do it together. 4 00:00:16,510 --> 00:00:17,080 All right. 5 00:00:17,230 --> 00:00:17,980 We are back. 6 00:00:18,040 --> 00:00:19,100 Let's do it together. 7 00:00:19,270 --> 00:00:25,430 You can see over here that this side is equal to this side and that's equal to the side right now. 8 00:00:25,990 --> 00:00:27,910 Over here, the case is the same. 9 00:00:27,910 --> 00:00:29,530 The side, the site and this side. 10 00:00:29,530 --> 00:00:31,540 These three sides are equal. 11 00:00:31,900 --> 00:00:32,250 Right. 12 00:00:32,380 --> 00:00:34,100 And it's inscribed in this circle. 13 00:00:34,120 --> 00:00:38,950 Now you can see that it's forming a regular hexagon, right? 14 00:00:39,130 --> 00:00:41,720 All these six sides are equal. 15 00:00:42,100 --> 00:00:45,130 And over here you have the diameter of the circle. 16 00:00:45,820 --> 00:00:48,130 Now, let's join this point. 17 00:00:48,130 --> 00:00:51,890 That is the center of the circle to these vertices over here. 18 00:00:52,790 --> 00:00:53,320 All right. 19 00:00:53,650 --> 00:00:56,200 Now, over here you have one, Topsham. 20 00:00:57,520 --> 00:01:04,460 And if I join these, what takes us to the midpoint, I get this over here, this divides the tropism 21 00:01:04,480 --> 00:01:08,650 over here into three equilateral triangles right now. 22 00:01:10,120 --> 00:01:18,820 Let me find the area of this regular hexagon that would be six times the area of one of the equilateral 23 00:01:18,820 --> 00:01:19,690 triangles, right. 24 00:01:19,870 --> 00:01:23,010 But that's Route three by four into a square. 25 00:01:23,290 --> 00:01:26,160 Over here, it's given that the diameter is 20 centimeter. 26 00:01:26,410 --> 00:01:30,760 Therefore, the side of this regular hexagon is equal to 10 centimeters. 27 00:01:30,760 --> 00:01:31,000 Right. 28 00:01:31,270 --> 00:01:32,510 This is equal to 20. 29 00:01:32,620 --> 00:01:35,140 So this much over here will be 10 centimeter. 30 00:01:36,120 --> 00:01:43,590 All right, so this is the area of this ship that is the regular hexagon, so that simplifies to 150 31 00:01:43,590 --> 00:01:45,690 route, three centimeter square. 32 00:01:45,970 --> 00:01:50,280 Now, we have seen how we can divide this into equal parts farther. 33 00:01:50,280 --> 00:01:50,610 Right. 34 00:01:50,820 --> 00:01:52,310 Let me draw these lines. 35 00:01:52,320 --> 00:01:54,840 I have one line over here, one over here and one over here. 36 00:01:55,140 --> 00:01:59,670 In this manner, we have divided this tropism into six equal parts. 37 00:02:00,090 --> 00:02:03,690 Right to one tropism is divided into six equal parts. 38 00:02:03,940 --> 00:02:11,550 If I do the same thing for the tropism below to trapezius would be divided into 12 equal parts to Trapezius 39 00:02:11,700 --> 00:02:14,280 or the regular hexagon we have seen before. 40 00:02:14,470 --> 00:02:18,140 All we can divide the regular hexagon into 12 equal parts. 41 00:02:18,150 --> 00:02:18,390 Right. 42 00:02:18,400 --> 00:02:21,420 You just need to extend these lines to this part as well. 43 00:02:21,720 --> 00:02:22,150 All right. 44 00:02:22,830 --> 00:02:26,900 Now, the question says that find the shaded area. 45 00:02:27,180 --> 00:02:29,100 So you just need to find this. 46 00:02:29,100 --> 00:02:30,510 Plus this, plus this. 47 00:02:30,510 --> 00:02:31,050 Plus this. 48 00:02:31,230 --> 00:02:37,470 So how many of the 12 equal parts do you need to take out so that you get what is asked in the question? 49 00:02:37,680 --> 00:02:40,440 You just need to take out these four parts, right. 50 00:02:40,590 --> 00:02:44,060 Or take out these four parts out of this part. 51 00:02:44,070 --> 00:02:44,340 Right. 52 00:02:44,350 --> 00:02:45,000 This area. 53 00:02:45,270 --> 00:02:49,770 So for that, you need to divide this area divided into 12 equal parts. 54 00:02:52,630 --> 00:03:01,270 And take out four parts to the answer would be or divided by 12 into 150 root three, and that is equal 55 00:03:01,270 --> 00:03:04,400 to 50 root three centimeter square. 56 00:03:04,540 --> 00:03:06,040 And that is your answer.