1 00:00:00,840 --> 00:00:08,790 Let's do this question and Sakalys inscribed in a square ABCDE inside the circle, another square BQ 2 00:00:08,790 --> 00:00:10,140 office is inscribed. 3 00:00:10,440 --> 00:00:12,950 The diameter of the circle is six centimeter. 4 00:00:13,260 --> 00:00:14,750 Find the shaded area. 5 00:00:15,030 --> 00:00:18,810 All right, pause the video, give it a try, and then let's do it together. 6 00:00:19,440 --> 00:00:19,950 All right. 7 00:00:20,160 --> 00:00:21,210 Let's get started. 8 00:00:21,330 --> 00:00:25,100 So we have a shaded part over here and a shaded part over here. 9 00:00:25,380 --> 00:00:27,950 So let me call this one and let me call this, too. 10 00:00:28,230 --> 00:00:30,280 Now, let's find one first. 11 00:00:30,600 --> 00:00:33,000 Now, one would be one by fort. 12 00:00:33,210 --> 00:00:37,310 The difference of the area of this square and this circle. 13 00:00:37,320 --> 00:00:38,010 Is that true? 14 00:00:38,250 --> 00:00:38,730 Right. 15 00:00:38,820 --> 00:00:39,300 That's true. 16 00:00:39,300 --> 00:00:39,600 Right. 17 00:00:39,720 --> 00:00:45,300 If I subtract the area of the square minus the area of the circle, I'll get this. 18 00:00:45,300 --> 00:00:47,430 Plus this, plus this, plus this. 19 00:00:47,430 --> 00:00:47,790 Right. 20 00:00:47,910 --> 00:00:49,110 And I just need this. 21 00:00:49,260 --> 00:00:54,820 So I need to take one by fort, the different of the area of the square and the circle. 22 00:00:55,050 --> 00:00:55,520 All right. 23 00:00:55,800 --> 00:01:01,590 Now, over here you can see that the diameter of the circle is equal to the side of the square, right. 24 00:01:01,800 --> 00:01:05,520 To draw the diameter like this, you can see that that's equal to eight. 25 00:01:05,670 --> 00:01:06,050 Right. 26 00:01:06,210 --> 00:01:09,860 So the diameter of the circle is equal to the side of ABCDE. 27 00:01:10,140 --> 00:01:15,250 Therefore, I know that the area of ABCDE is six to six right over here. 28 00:01:15,270 --> 00:01:16,260 This is given a six. 29 00:01:16,290 --> 00:01:17,780 So this is also equal to six. 30 00:01:18,060 --> 00:01:24,210 So area of ABCDE will be six in the six and over here as their diameter is six, the radius will be 31 00:01:24,210 --> 00:01:24,590 three. 32 00:01:24,810 --> 00:01:28,530 Therefore the area of the circle is bindu three square. 33 00:01:28,830 --> 00:01:33,500 So this is one by four to six square minus by into three square. 34 00:01:33,690 --> 00:01:35,550 That gives you this shaded region. 35 00:01:35,550 --> 00:01:35,880 Right. 36 00:01:36,040 --> 00:01:40,230 And this is equal to thirty six minus nine pi divided by four. 37 00:01:40,530 --> 00:01:42,630 All right, let's find the second part. 38 00:01:42,930 --> 00:01:48,080 This would be one by fourth, the area of the circle minus the area of the square. 39 00:01:48,090 --> 00:01:48,450 Right. 40 00:01:48,690 --> 00:01:53,880 Because if you subtract the area of the circle and then minus the area of the square, you'll get this 41 00:01:54,090 --> 00:01:55,740 plus this, plus this, plus this. 42 00:01:55,740 --> 00:01:56,040 Right. 43 00:01:56,160 --> 00:01:57,320 And you just need this. 44 00:01:57,450 --> 00:01:59,040 So you need to take one by fourth. 45 00:01:59,340 --> 00:02:05,150 So this over here will be one by fourth area of the circle, minus area of BQ. 46 00:02:05,160 --> 00:02:06,000 Q Right. 47 00:02:06,270 --> 00:02:12,900 And over here we know that the area of the circle is nine five and the area of P you are, as we have 48 00:02:12,900 --> 00:02:16,060 seen, will be half of the area of ABCDE. 49 00:02:16,140 --> 00:02:16,450 Right. 50 00:02:16,710 --> 00:02:20,370 So that would be half of area of a city. 51 00:02:20,370 --> 00:02:21,840 That's half of 36. 52 00:02:21,990 --> 00:02:22,360 Right. 53 00:02:22,530 --> 00:02:26,820 So this becomes one by fort of nine by minus 18. 54 00:02:27,120 --> 00:02:27,560 All right. 55 00:02:27,780 --> 00:02:29,520 So now we have this and this. 56 00:02:29,700 --> 00:02:32,880 Now the answer would be this plus this, right? 57 00:02:33,090 --> 00:02:35,060 Because we need this and this together. 58 00:02:35,250 --> 00:02:43,190 So one and two together gives one by four out of thirty six minus nine by plus nine by minus 18. 59 00:02:43,320 --> 00:02:44,970 And that is equal to. 60 00:02:46,010 --> 00:02:49,760 Eighteen by four or nine by two centimeter square. 61 00:02:50,700 --> 00:02:52,470 And that is a solution to this question. 62 00:02:52,790 --> 00:02:56,760 Now let's see one more approach in which this could have been done over here. 63 00:02:56,760 --> 00:03:00,210 You can see that this distance is half of it. 64 00:03:00,360 --> 00:03:01,970 That's Aebi, too, right? 65 00:03:02,850 --> 00:03:05,340 Similarly, this is also half of. 66 00:03:05,940 --> 00:03:09,600 So this is also able to right this part over here. 67 00:03:09,610 --> 00:03:16,920 If you join this together, this would be of length route to into EBITA or Ebeye. 68 00:03:17,100 --> 00:03:17,600 Route to. 69 00:03:17,670 --> 00:03:18,050 Right. 70 00:03:18,270 --> 00:03:23,940 Therefore, you can see that you can actually rotate this square over here and it will look like this. 71 00:03:24,180 --> 00:03:24,520 Right. 72 00:03:24,690 --> 00:03:27,710 The site of this square also is a by route to. 73 00:03:27,750 --> 00:03:28,110 Right. 74 00:03:28,200 --> 00:03:33,750 And that's why the area of the square we saw is half the area of the outer square because the area is 75 00:03:33,750 --> 00:03:37,860 able to do able to that's equal to a square by two. 76 00:03:37,980 --> 00:03:40,220 That is half of the area of the outer square. 77 00:03:40,430 --> 00:03:46,680 But this site also is able to and we have seen this is also able to so you can actually rotated and 78 00:03:46,680 --> 00:03:47,810 then it look like this. 79 00:03:48,000 --> 00:03:57,840 Now you just need to take one by fourth of the difference of the area of ABCDE and Bhiku Orris, this 80 00:03:57,840 --> 00:03:58,540 one over here. 81 00:03:58,560 --> 00:03:58,920 Right. 82 00:03:59,100 --> 00:03:59,700 Why is that? 83 00:03:59,700 --> 00:04:06,570 So if you subtract the area of ABCDE and then from that you subtract this part, you are left with this, 84 00:04:06,570 --> 00:04:08,160 plus this, plus this, plus this. 85 00:04:08,340 --> 00:04:10,080 And this is one bifold of that. 86 00:04:10,080 --> 00:04:10,440 Right. 87 00:04:10,650 --> 00:04:11,010 All right. 88 00:04:11,010 --> 00:04:12,570 Let me make some space over here. 89 00:04:12,830 --> 00:04:18,220 So that is equal to one by fourth of half of the area of ABCDE. 90 00:04:18,390 --> 00:04:19,210 Why is that so? 91 00:04:19,440 --> 00:04:25,130 Because the area we saw of Piku Outis is half the area of ABCDE. 92 00:04:25,320 --> 00:04:28,440 So if you subtract area of ABCDE. 93 00:04:29,590 --> 00:04:32,800 Minus area of BQ Orris. 94 00:04:34,350 --> 00:04:37,110 You can write this as area of ABCDE. 95 00:04:38,360 --> 00:04:46,400 Minus area of ebiquity by two, right, because we have seen that area of procuracy will be half the 96 00:04:46,400 --> 00:04:53,450 area of ABCDE, when you do this subtraction, you get area of ABCDE by two and you need to take one 97 00:04:53,450 --> 00:04:55,630 by fourth of that because you just need that. 98 00:04:55,640 --> 00:04:56,120 All right. 99 00:04:56,430 --> 00:05:00,110 So this area over here is equal to six into six. 100 00:05:00,320 --> 00:05:01,020 So that's six. 101 00:05:01,130 --> 00:05:03,290 The six by two into one by four. 102 00:05:03,380 --> 00:05:03,740 Right. 103 00:05:03,980 --> 00:05:07,460 And what is the answer that you get that is equal to. 104 00:05:08,960 --> 00:05:13,570 Nine by two, right, one by four into one by two in the six in the six. 105 00:05:13,790 --> 00:05:16,700 That gives you nine by two centimeter square. 106 00:05:16,820 --> 00:05:19,460 And that is the same answer that we got before.