[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.61,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.61,0:00:03.56,Default,,0000,0000,0000,,What is the area of this figure?
Dialogue: 0,0:00:03.56,0:00:05.39,Default,,0000,0000,0000,,And this figure right\Nover here is sometimes
Dialogue: 0,0:00:05.39,0:00:07.22,Default,,0000,0000,0000,,called a kite for\Nobvious reasons.
Dialogue: 0,0:00:07.22,0:00:08.60,Default,,0000,0000,0000,,If you tied some\Nstring here, you
Dialogue: 0,0:00:08.60,0:00:10.05,Default,,0000,0000,0000,,might want to fly\Nit at the beach.
Dialogue: 0,0:00:10.05,0:00:11.97,Default,,0000,0000,0000,,And another way to think\Nabout what a kite is,
Dialogue: 0,0:00:11.97,0:00:20.90,Default,,0000,0000,0000,,it's a quadrilateral that is\Nsymmetric around a diagonal.
Dialogue: 0,0:00:20.90,0:00:24.35,Default,,0000,0000,0000,,So this right over here is the\Ndiagonal of this quadrilateral.
Dialogue: 0,0:00:24.35,0:00:25.91,Default,,0000,0000,0000,,And it's symmetric around it.
Dialogue: 0,0:00:25.91,0:00:29.96,Default,,0000,0000,0000,,This top part and this bottom\Npart are mirror images.
Dialogue: 0,0:00:29.96,0:00:32.08,Default,,0000,0000,0000,,And to think about how we\Nmight find the area of it
Dialogue: 0,0:00:32.08,0:00:34.20,Default,,0000,0000,0000,,given that we've been\Ngiven essentially
Dialogue: 0,0:00:34.20,0:00:36.77,Default,,0000,0000,0000,,the width of this\Nkite, and we've also
Dialogue: 0,0:00:36.77,0:00:39.12,Default,,0000,0000,0000,,been given the\Nheight of this kite,
Dialogue: 0,0:00:39.12,0:00:41.09,Default,,0000,0000,0000,,or if you view this\Nas a sideways kite,
Dialogue: 0,0:00:41.09,0:00:42.89,Default,,0000,0000,0000,,you could view this\Nis the height and that
Dialogue: 0,0:00:42.89,0:00:44.95,Default,,0000,0000,0000,,the eight centimeters\Nas the width.
Dialogue: 0,0:00:44.95,0:00:46.66,Default,,0000,0000,0000,,Given that we've got\Nthose dimensions,
Dialogue: 0,0:00:46.66,0:00:49.40,Default,,0000,0000,0000,,how can we actually\Nfigure out its area?
Dialogue: 0,0:00:49.40,0:00:52.57,Default,,0000,0000,0000,,So to do that, let\Nme actually copy
Dialogue: 0,0:00:52.57,0:00:53.92,Default,,0000,0000,0000,,and paste half of the kite.
Dialogue: 0,0:00:53.92,0:00:56.18,Default,,0000,0000,0000,,So this is the bottom\Nhalf of the kite.
Dialogue: 0,0:00:56.18,0:01:01.53,Default,,0000,0000,0000,,And then let's take the\Ntop half of the kite
Dialogue: 0,0:01:01.53,0:01:03.45,Default,,0000,0000,0000,,and split it up into sections.
Dialogue: 0,0:01:03.45,0:01:06.56,Default,,0000,0000,0000,,So I have this little\Nred section here.
Dialogue: 0,0:01:06.56,0:01:08.41,Default,,0000,0000,0000,,I have this red section here.
Dialogue: 0,0:01:08.41,0:01:15.56,Default,,0000,0000,0000,,And actually, I'm going to try\Nto color the actual lines here
Dialogue: 0,0:01:15.56,0:01:18.01,Default,,0000,0000,0000,,so that we can keep\Ntrack of those as well.
Dialogue: 0,0:01:18.01,0:01:23.91,Default,,0000,0000,0000,,So I'll make this line green\Nand I'll make this line purple.
Dialogue: 0,0:01:23.91,0:01:27.29,Default,,0000,0000,0000,,So imagine taking this little\Ntriangle right over here--
Dialogue: 0,0:01:27.29,0:01:31.02,Default,,0000,0000,0000,,and actually, let me do\Nthis one too in blue.
Dialogue: 0,0:01:31.02,0:01:34.63,Default,,0000,0000,0000,,So this one over here is blue.
Dialogue: 0,0:01:34.63,0:01:35.51,Default,,0000,0000,0000,,You get the picture.
Dialogue: 0,0:01:35.51,0:01:37.70,Default,,0000,0000,0000,,Let me try to color it\Nin at least reasonably.
Dialogue: 0,0:01:37.70,0:01:38.78,Default,,0000,0000,0000,,So I'll color it in.
Dialogue: 0,0:01:38.78,0:01:44.62,Default,,0000,0000,0000,,And then I could make this\Nsegment right over here,
Dialogue: 0,0:01:44.62,0:01:46.84,Default,,0000,0000,0000,,I'm going to make orange.
Dialogue: 0,0:01:46.84,0:01:49.54,Default,,0000,0000,0000,,So let's start focusing\Non this red triangle here.
Dialogue: 0,0:01:49.54,0:01:57.80,Default,,0000,0000,0000,,Imagine flipping it over and\Nthen moving it down here.
Dialogue: 0,0:01:57.80,0:01:59.38,Default,,0000,0000,0000,,So what would it look like?
Dialogue: 0,0:01:59.38,0:02:04.23,Default,,0000,0000,0000,,Well then the green side is\Ngoing to now be over here.
Dialogue: 0,0:02:04.23,0:02:08.34,Default,,0000,0000,0000,,This kind of mauve colored\Nside is still on the bottom.
Dialogue: 0,0:02:08.34,0:02:12.58,Default,,0000,0000,0000,,And my red triangle is going\Nto look something like this.
Dialogue: 0,0:02:12.58,0:02:15.94,Default,,0000,0000,0000,,My red triangle is\Ngoing to look like that.
Dialogue: 0,0:02:15.94,0:02:19.09,Default,,0000,0000,0000,,Now let's do the same thing\Nwith this bigger blue triangle.
Dialogue: 0,0:02:19.09,0:02:22.75,Default,,0000,0000,0000,,Let's flip it over and\Nthen move it down here.
Dialogue: 0,0:02:22.75,0:02:28.05,Default,,0000,0000,0000,,So this green side, since we've\Nflipped it, is now over here.
Dialogue: 0,0:02:28.05,0:02:32.62,Default,,0000,0000,0000,,And this orange side\Nis now over here.
Dialogue: 0,0:02:32.62,0:02:35.48,Default,,0000,0000,0000,,
Dialogue: 0,0:02:35.48,0:02:42.68,Default,,0000,0000,0000,,And we have this\Nblue right over here.
Dialogue: 0,0:02:42.68,0:02:45.16,Default,,0000,0000,0000,,And the reason that we know\Nthat it definitely fits
Dialogue: 0,0:02:45.16,0:02:48.36,Default,,0000,0000,0000,,is the fact that it is\Nsymmetric around this diagonal,
Dialogue: 0,0:02:48.36,0:02:50.56,Default,,0000,0000,0000,,that this length\Nright over here is
Dialogue: 0,0:02:50.56,0:02:54.42,Default,,0000,0000,0000,,equivalent to this\Nlength right over here.
Dialogue: 0,0:02:54.42,0:02:57.22,Default,,0000,0000,0000,,That's why it fits\Nperfectly like this.
Dialogue: 0,0:02:57.22,0:02:59.51,Default,,0000,0000,0000,,Now, what we just\Nconstructed is clearly
Dialogue: 0,0:02:59.51,0:03:06.80,Default,,0000,0000,0000,,a rectangle, a rectangle that\Nis 14 centimeters wide and not
Dialogue: 0,0:03:06.80,0:03:10.49,Default,,0000,0000,0000,,8 centimeters high, it's\Nhalf of 8 centimeters high.
Dialogue: 0,0:03:10.49,0:03:14.89,Default,,0000,0000,0000,,So it's 8 centimeters times\N1/2 or 4 centimeters high.
Dialogue: 0,0:03:14.89,0:03:17.03,Default,,0000,0000,0000,,And we know how to\Nfind the area of this.
Dialogue: 0,0:03:17.03,0:03:20.49,Default,,0000,0000,0000,,This is 4 centimeters\Ntimes 14 centimeters.
Dialogue: 0,0:03:20.49,0:03:25.46,Default,,0000,0000,0000,,So the area is equal\Nto 4 centimeters
Dialogue: 0,0:03:25.46,0:03:30.24,Default,,0000,0000,0000,,times 14 centimeters which\Nis equal to-- let's see,
Dialogue: 0,0:03:30.24,0:03:35.64,Default,,0000,0000,0000,,that's 40 plus 16--\N56 square centimeters.
Dialogue: 0,0:03:35.64,0:03:37.59,Default,,0000,0000,0000,,So if you're taking\Nthe area of a kite,
Dialogue: 0,0:03:37.59,0:03:41.37,Default,,0000,0000,0000,,you're really just\Ntaking 1/2 the width
Dialogue: 0,0:03:41.37,0:03:45.41,Default,,0000,0000,0000,,times the height, or 1/2\Nthe width times the height,
Dialogue: 0,0:03:45.41,0:03:48.54,Default,,0000,0000,0000,,any way you want\Nto think about it.