WEBVTT 00:00:00.000 --> 00:00:00.610 00:00:00.610 --> 00:00:03.557 What is the area of this figure? 00:00:03.557 --> 00:00:05.390 And this figure right over here is sometimes 00:00:05.390 --> 00:00:07.225 called a kite for obvious reasons. 00:00:07.225 --> 00:00:08.600 If you tied some string here, you 00:00:08.600 --> 00:00:10.054 might want to fly it at the beach. 00:00:10.054 --> 00:00:11.970 And another way to think about what a kite is, 00:00:11.970 --> 00:00:20.900 it's a quadrilateral that is symmetric around a diagonal. 00:00:20.900 --> 00:00:24.350 So this right over here is the diagonal of this quadrilateral. 00:00:24.350 --> 00:00:25.910 And it's symmetric around it. 00:00:25.910 --> 00:00:29.955 This top part and this bottom part are mirror images. 00:00:29.955 --> 00:00:32.080 And to think about how we might find the area of it 00:00:32.080 --> 00:00:34.200 given that we've been given essentially 00:00:34.200 --> 00:00:36.770 the width of this kite, and we've also 00:00:36.770 --> 00:00:39.120 been given the height of this kite, 00:00:39.120 --> 00:00:41.090 or if you view this as a sideways kite, 00:00:41.090 --> 00:00:42.890 you could view this is the height and that 00:00:42.890 --> 00:00:44.950 the eight centimeters as the width. 00:00:44.950 --> 00:00:46.660 Given that we've got those dimensions, 00:00:46.660 --> 00:00:49.400 how can we actually figure out its area? 00:00:49.400 --> 00:00:52.570 So to do that, let me actually copy 00:00:52.570 --> 00:00:53.920 and paste half of the kite. 00:00:53.920 --> 00:00:56.180 So this is the bottom half of the kite. 00:00:56.180 --> 00:01:01.530 And then let's take the top half of the kite 00:01:01.530 --> 00:01:03.450 and split it up into sections. 00:01:03.450 --> 00:01:06.560 So I have this little red section here. 00:01:06.560 --> 00:01:08.410 I have this red section here. 00:01:08.410 --> 00:01:15.560 And actually, I'm going to try to color the actual lines here 00:01:15.560 --> 00:01:18.010 so that we can keep track of those as well. 00:01:18.010 --> 00:01:23.910 So I'll make this line green and I'll make this line purple. 00:01:23.910 --> 00:01:27.290 So imagine taking this little triangle right over here-- 00:01:27.290 --> 00:01:31.020 and actually, let me do this one too in blue. 00:01:31.020 --> 00:01:34.630 So this one over here is blue. 00:01:34.630 --> 00:01:35.510 You get the picture. 00:01:35.510 --> 00:01:37.695 Let me try to color it in at least reasonably. 00:01:37.695 --> 00:01:38.780 So I'll color it in. 00:01:38.780 --> 00:01:44.620 And then I could make this segment right over here, 00:01:44.620 --> 00:01:46.840 I'm going to make orange. 00:01:46.840 --> 00:01:49.540 So let's start focusing on this red triangle here. 00:01:49.540 --> 00:01:57.800 Imagine flipping it over and then moving it down here. 00:01:57.800 --> 00:01:59.380 So what would it look like? 00:01:59.380 --> 00:02:04.230 Well then the green side is going to now be over here. 00:02:04.230 --> 00:02:08.340 This kind of mauve colored side is still on the bottom. 00:02:08.340 --> 00:02:12.580 And my red triangle is going to look something like this. 00:02:12.580 --> 00:02:15.940 My red triangle is going to look like that. 00:02:15.940 --> 00:02:19.090 Now let's do the same thing with this bigger blue triangle. 00:02:19.090 --> 00:02:22.750 Let's flip it over and then move it down here. 00:02:22.750 --> 00:02:28.050 So this green side, since we've flipped it, is now over here. 00:02:28.050 --> 00:02:32.615 And this orange side is now over here. 00:02:32.615 --> 00:02:35.480 00:02:35.480 --> 00:02:42.680 And we have this blue right over here. 00:02:42.680 --> 00:02:45.160 And the reason that we know that it definitely fits 00:02:45.160 --> 00:02:48.360 is the fact that it is symmetric around this diagonal, 00:02:48.360 --> 00:02:50.560 that this length right over here is 00:02:50.560 --> 00:02:54.420 equivalent to this length right over here. 00:02:54.420 --> 00:02:57.220 That's why it fits perfectly like this. 00:02:57.220 --> 00:02:59.510 Now, what we just constructed is clearly 00:02:59.510 --> 00:03:06.800 a rectangle, a rectangle that is 14 centimeters wide and not 00:03:06.800 --> 00:03:10.490 8 centimeters high, it's half of 8 centimeters high. 00:03:10.490 --> 00:03:14.890 So it's 8 centimeters times 1/2 or 4 centimeters high. 00:03:14.890 --> 00:03:17.030 And we know how to find the area of this. 00:03:17.030 --> 00:03:20.490 This is 4 centimeters times 14 centimeters. 00:03:20.490 --> 00:03:25.460 So the area is equal to 4 centimeters 00:03:25.460 --> 00:03:30.240 times 14 centimeters which is equal to-- let's see, 00:03:30.240 --> 00:03:35.640 that's 40 plus 16-- 56 square centimeters. 00:03:35.640 --> 00:03:37.590 So if you're taking the area of a kite, 00:03:37.590 --> 00:03:41.370 you're really just taking 1/2 the width 00:03:41.370 --> 00:03:45.410 times the height, or 1/2 the width times the height, 00:03:45.410 --> 00:03:48.540 any way you want to think about it.