[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.83,0:00:03.00,Default,,0000,0000,0000,,I've got a square here.
Dialogue: 0,0:00:04.79,0:00:08.06,Default,,0000,0000,0000,,What makes it a square is\Nall of the sides are equal.
Dialogue: 0,0:00:08.06,0:00:10.38,Default,,0000,0000,0000,,I haven't gone in depth into\Nangles yet, but these are at
Dialogue: 0,0:00:10.38,0:00:12.52,Default,,0000,0000,0000,,right angles to each other.
Dialogue: 0,0:00:12.52,0:00:13.47,Default,,0000,0000,0000,,I'll just draw it like that.
Dialogue: 0,0:00:13.47,0:00:16.76,Default,,0000,0000,0000,,That means that if this bottom\Nside goes straight left and
Dialogue: 0,0:00:16.76,0:00:19.88,Default,,0000,0000,0000,,right, that this left side\Nwill go straight up and down.
Dialogue: 0,0:00:19.88,0:00:22.21,Default,,0000,0000,0000,,That's all the right\Nangle really means.
Dialogue: 0,0:00:22.21,0:00:27.29,Default,,0000,0000,0000,,Let's say that the side down\Nhere is equal to 8 meters.
Dialogue: 0,0:00:27.29,0:00:28.54,Default,,0000,0000,0000,,This side right here.
Dialogue: 0,0:00:28.54,0:00:30.10,Default,,0000,0000,0000,,And this is a square.
Dialogue: 0,0:00:30.10,0:00:35.98,Default,,0000,0000,0000,,And I were to ask you what\Nis the area of the square?
Dialogue: 0,0:00:35.98,0:00:39.04,Default,,0000,0000,0000,,Well, the area is essentially\Nhow much space the square
Dialogue: 0,0:00:39.04,0:00:41.43,Default,,0000,0000,0000,,takes up, let's say, on\Nyour screen right now.
Dialogue: 0,0:00:41.43,0:00:46.04,Default,,0000,0000,0000,,So it's essentially a way of\Nmeasuring how much space
Dialogue: 0,0:00:46.04,0:00:49.11,Default,,0000,0000,0000,,something takes up on kind of\Na two-dimensional surface.
Dialogue: 0,0:00:49.11,0:00:52.17,Default,,0000,0000,0000,,A two-dimensional surface would\Njust be this computer screen or
Dialogue: 0,0:00:52.17,0:00:55.53,Default,,0000,0000,0000,,your piece of paper, if you're\Nalso doing this problem.
Dialogue: 0,0:00:55.53,0:00:58.68,Default,,0000,0000,0000,,An analogy would be if you had\Nan 8 meter by 8 meter room, how
Dialogue: 0,0:00:58.68,0:01:01.57,Default,,0000,0000,0000,,much carpeting would you need\Nis kind of the size of the
Dialogue: 0,0:01:01.57,0:01:04.24,Default,,0000,0000,0000,,space you need to fill out in\Ntwo dimensions on some
Dialogue: 0,0:01:04.24,0:01:05.50,Default,,0000,0000,0000,,type of surface.
Dialogue: 0,0:01:05.50,0:01:09.75,Default,,0000,0000,0000,,So the area here is literally\Nhow much is this size that
Dialogue: 0,0:01:09.75,0:01:11.98,Default,,0000,0000,0000,,you're filling up, and it's\Nvery easy to figure
Dialogue: 0,0:01:11.98,0:01:12.60,Default,,0000,0000,0000,,out for a square.
Dialogue: 0,0:01:12.60,0:01:15.83,Default,,0000,0000,0000,,It's literally going to be your\Nbase times your height -- and
Dialogue: 0,0:01:15.83,0:01:18.57,Default,,0000,0000,0000,,this is true for any rectangle\N-- but since this is a square,
Dialogue: 0,0:01:18.57,0:01:20.65,Default,,0000,0000,0000,,your base and your height are\Ngoing to be the same number.
Dialogue: 0,0:01:20.65,0:01:22.34,Default,,0000,0000,0000,,It's going to be 8 meters.
Dialogue: 0,0:01:22.34,0:01:27.93,Default,,0000,0000,0000,,So your area is going to be 8\Nmeters times 8 meters, which is
Dialogue: 0,0:01:27.93,0:01:32.02,Default,,0000,0000,0000,,equal to 8 times 8 is 64, and\Nthen your meters times your
Dialogue: 0,0:01:32.02,0:01:34.58,Default,,0000,0000,0000,,meters -- you have to do the\Nsame thing with your units --
Dialogue: 0,0:01:34.58,0:01:37.20,Default,,0000,0000,0000,,you get 64 meters squared.
Dialogue: 0,0:01:37.20,0:01:40.86,Default,,0000,0000,0000,,Or another way of saying,\Nthis is 64 square meters.
Dialogue: 0,0:01:40.86,0:01:44.39,Default,,0000,0000,0000,,You might be asking where\Nare those 64 square meters?
Dialogue: 0,0:01:44.39,0:01:46.62,Default,,0000,0000,0000,,Well, you can actually\Nbreak it out here.
Dialogue: 0,0:01:46.62,0:01:48.47,Default,,0000,0000,0000,,So let me draw it a\Nlittle bit bigger than
Dialogue: 0,0:01:48.47,0:01:49.63,Default,,0000,0000,0000,,I originally drew it.
Dialogue: 0,0:01:49.63,0:01:51.89,Default,,0000,0000,0000,,I probably should have drawn\Nit this big to begin with.
Dialogue: 0,0:01:51.89,0:01:55.94,Default,,0000,0000,0000,,So let's say that's\Nmy same square.
Dialogue: 0,0:01:55.94,0:01:58.10,Default,,0000,0000,0000,,I'm going to draw a little\Nbit, so let me divide
Dialogue: 0,0:01:58.10,0:02:00.24,Default,,0000,0000,0000,,it in the middle.
Dialogue: 0,0:02:00.24,0:02:03.77,Default,,0000,0000,0000,,Let me see, I have -- and\Nwe divide them again.
Dialogue: 0,0:02:03.77,0:02:07.14,Default,,0000,0000,0000,,Then we divide each side\Nagain just like that.
Dialogue: 0,0:02:07.14,0:02:08.41,Default,,0000,0000,0000,,I could probably do it neater.
Dialogue: 0,0:02:08.41,0:02:10.93,Default,,0000,0000,0000,,And let me do it one more time.
Dialogue: 0,0:02:10.93,0:02:16.84,Default,,0000,0000,0000,,Divide these just like that,\Nand then divide these
Dialogue: 0,0:02:16.84,0:02:19.01,Default,,0000,0000,0000,,just like that.
Dialogue: 0,0:02:19.01,0:02:20.94,Default,,0000,0000,0000,,There you go.
Dialogue: 0,0:02:20.94,0:02:21.48,Default,,0000,0000,0000,,OK.
Dialogue: 0,0:02:21.48,0:02:23.98,Default,,0000,0000,0000,,Now the reason why I did this\Nis to show you the dimensions
Dialogue: 0,0:02:23.98,0:02:27.03,Default,,0000,0000,0000,,along the base and the height.
Dialogue: 0,0:02:27.03,0:02:30.65,Default,,0000,0000,0000,,We said this is 8 meters,\Nand notice I have 1, 2,
Dialogue: 0,0:02:30.65,0:02:34.61,Default,,0000,0000,0000,,3, 4, 5, 6, 7, 8 meters.
Dialogue: 0,0:02:34.61,0:02:36.62,Default,,0000,0000,0000,,And the same thing\Nalong this side.
Dialogue: 0,0:02:36.62,0:02:42.05,Default,,0000,0000,0000,,1, 2, 3, 4, 5, 6, 7, 8 meters.
Dialogue: 0,0:02:42.05,0:02:45.34,Default,,0000,0000,0000,,So when we're talking about\N64 square meters, we're
Dialogue: 0,0:02:45.34,0:02:47.52,Default,,0000,0000,0000,,literally counting each\Nof the square meters.
Dialogue: 0,0:02:47.52,0:02:50.38,Default,,0000,0000,0000,,A square meter is a\Ntwo-dimensional measurement,
Dialogue: 0,0:02:50.38,0:02:51.78,Default,,0000,0000,0000,,that's 1 meter on each side.
Dialogue: 0,0:02:51.78,0:02:53.49,Default,,0000,0000,0000,,That's 1 meter, that's 1 meter.
Dialogue: 0,0:02:53.49,0:02:56.48,Default,,0000,0000,0000,,What I'm shading here in\Nyellow is 1 square meter.
Dialogue: 0,0:02:56.48,0:02:59.03,Default,,0000,0000,0000,,And you could imagine just\Ncounting the square meters.
Dialogue: 0,0:02:59.03,0:03:05.07,Default,,0000,0000,0000,,In each row we're going to\Nhave 1, 2, 3, 4, 5, 6,
Dialogue: 0,0:03:05.07,0:03:07.08,Default,,0000,0000,0000,,7, 8 square meters.
Dialogue: 0,0:03:07.08,0:03:08.61,Default,,0000,0000,0000,,And then we have 8 rows.
Dialogue: 0,0:03:08.61,0:03:11.20,Default,,0000,0000,0000,,So we're going to have 8\Ntimes 8 square meters
Dialogue: 0,0:03:11.20,0:03:12.76,Default,,0000,0000,0000,,or 64 meters square.
Dialogue: 0,0:03:12.76,0:03:14.84,Default,,0000,0000,0000,,Which is essentially if you sat\Nhere and just counted each of
Dialogue: 0,0:03:14.84,0:03:19.05,Default,,0000,0000,0000,,these, you would count\N64 square meters.
Dialogue: 0,0:03:19.05,0:03:21.54,Default,,0000,0000,0000,,Now, what happens if I\Nwere to ask you the
Dialogue: 0,0:03:21.54,0:03:24.69,Default,,0000,0000,0000,,perimeter of my square?
Dialogue: 0,0:03:28.00,0:03:30.62,Default,,0000,0000,0000,,The perimeter is the distance\Nyou need to go to go
Dialogue: 0,0:03:30.62,0:03:31.95,Default,,0000,0000,0000,,around the square.
Dialogue: 0,0:03:31.95,0:03:33.99,Default,,0000,0000,0000,,It's not measuring,\Nfor example, how much
Dialogue: 0,0:03:33.99,0:03:35.07,Default,,0000,0000,0000,,carpeting you need.
Dialogue: 0,0:03:35.07,0:03:37.52,Default,,0000,0000,0000,,It's measuring, for example, if\Nyou wanted to put a fence
Dialogue: 0,0:03:37.52,0:03:40.05,Default,,0000,0000,0000,,around your carpet -- I'm kind\Nof mixing the indoor and
Dialogue: 0,0:03:40.05,0:03:42.40,Default,,0000,0000,0000,,outdoor analogies -- it would\Nbe how much fencing
Dialogue: 0,0:03:42.40,0:03:43.11,Default,,0000,0000,0000,,you would need.
Dialogue: 0,0:03:43.11,0:03:46.21,Default,,0000,0000,0000,,So it would be the\Ndistance around.
Dialogue: 0,0:03:46.21,0:03:48.95,Default,,0000,0000,0000,,So it would be that distance\Nplus that distance plus that
Dialogue: 0,0:03:48.95,0:03:50.98,Default,,0000,0000,0000,,distance plus that distance.
Dialogue: 0,0:03:50.98,0:03:53.83,Default,,0000,0000,0000,,But we already know this\Ndistance right here on the
Dialogue: 0,0:03:53.83,0:03:58.02,Default,,0000,0000,0000,,bottom, we already know\Nthis distance is 8 meters.
Dialogue: 0,0:03:58.02,0:04:01.48,Default,,0000,0000,0000,,Then we know that the height\Nright here is 8 meters.
Dialogue: 0,0:04:01.48,0:04:02.18,Default,,0000,0000,0000,,It's a square.
Dialogue: 0,0:04:02.18,0:04:04.57,Default,,0000,0000,0000,,This distance up here is going\Nto be the same as this distance
Dialogue: 0,0:04:04.57,0:04:07.71,Default,,0000,0000,0000,,down here -- it's going\Nto be another 8 meters.
Dialogue: 0,0:04:07.71,0:04:09.45,Default,,0000,0000,0000,,Then when you go down the\Nleft hand side it's going
Dialogue: 0,0:04:09.45,0:04:11.38,Default,,0000,0000,0000,,to be another 8 meters.
Dialogue: 0,0:04:11.38,0:04:15.67,Default,,0000,0000,0000,,We have four sides -- 1, 2, 3,\N4 -- each of them are 8 meters.
Dialogue: 0,0:04:15.67,0:04:18.66,Default,,0000,0000,0000,,So you add 8 to itself 4 times,\Nthat's the same thing as 8
Dialogue: 0,0:04:18.66,0:04:21.07,Default,,0000,0000,0000,,times 4, you get 36 meters.
Dialogue: 0,0:04:21.07,0:04:25.05,Default,,0000,0000,0000,,Now notice, when we measured\Njust the amount of fencing we
Dialogue: 0,0:04:25.05,0:04:28.53,Default,,0000,0000,0000,,needed, we ended up just with\Nmeters, just with kind of a
Dialogue: 0,0:04:28.53,0:04:30.68,Default,,0000,0000,0000,,one-dimensional measurement.
Dialogue: 0,0:04:30.68,0:04:33.08,Default,,0000,0000,0000,,That's because we're not\Nmeasuring square meters here.
Dialogue: 0,0:04:33.08,0:04:35.31,Default,,0000,0000,0000,,We're not measuring how\Nmuch area we're taking up.
Dialogue: 0,0:04:35.31,0:04:38.56,Default,,0000,0000,0000,,We're measuring a distance\N-- a distance to go around.
Dialogue: 0,0:04:38.56,0:04:40.92,Default,,0000,0000,0000,,We are taking turns, but you\Ncan imagine straightening out
Dialogue: 0,0:04:40.92,0:04:44.57,Default,,0000,0000,0000,,this fence, and it would just\Nbecome one big fence like this,
Dialogue: 0,0:04:44.57,0:04:48.16,Default,,0000,0000,0000,,which would have the same\Nlength of 36 meters.
Dialogue: 0,0:04:48.16,0:04:51.01,Default,,0000,0000,0000,,So that's why we just have\Nmeters there for perimeter.
Dialogue: 0,0:04:51.01,0:04:53.64,Default,,0000,0000,0000,,But for area we got square\Nmeters, because we're counting
Dialogue: 0,0:04:53.64,0:04:56.22,Default,,0000,0000,0000,,these two-dimensional\Nmeasurements.
Dialogue: 0,0:04:56.22,0:04:58.84,Default,,0000,0000,0000,,Now, let's make it a little\Nbit more interesting.
Dialogue: 0,0:04:58.84,0:05:02.07,Default,,0000,0000,0000,,What happens if instead\Nof a square I have a
Dialogue: 0,0:05:02.07,0:05:05.78,Default,,0000,0000,0000,,rectangle like this?
Dialogue: 0,0:05:09.70,0:05:15.28,Default,,0000,0000,0000,,Let's say that this side\Nover here is 7 centimeters.
Dialogue: 0,0:05:15.28,0:05:23.17,Default,,0000,0000,0000,,And let's say that the height\Nright here is 4 centimeters.
Dialogue: 0,0:05:23.17,0:05:25.84,Default,,0000,0000,0000,,So what is the area of this\Nrectangle going to be?
Dialogue: 0,0:05:25.84,0:05:28.28,Default,,0000,0000,0000,,It's going to be 7\Ntimes 4 centimeters.
Dialogue: 0,0:05:28.28,0:05:31.49,Default,,0000,0000,0000,,7 centimeters times\N4 centimeters.
Dialogue: 0,0:05:31.49,0:05:36.39,Default,,0000,0000,0000,,Remember, we could draw 7 rows,\Nright, and each of them is
Dialogue: 0,0:05:36.39,0:05:39.54,Default,,0000,0000,0000,,going to have 4 square\Ncentimeters -- each of those
Dialogue: 0,0:05:39.54,0:05:40.38,Default,,0000,0000,0000,,is a square centimeter.
Dialogue: 0,0:05:40.38,0:05:42.36,Default,,0000,0000,0000,,So if you were to count them\Nall out, you'd have 7 times
Dialogue: 0,0:05:42.36,0:05:44.17,Default,,0000,0000,0000,,4 square centimeters.
Dialogue: 0,0:05:44.17,0:05:45.14,Default,,0000,0000,0000,,It's 4 centimeters.
Dialogue: 0,0:05:45.14,0:05:50.39,Default,,0000,0000,0000,,So it's equal to 28 centimeters\Nsquare or squared centimeters.
Dialogue: 0,0:05:50.39,0:05:51.07,Default,,0000,0000,0000,,What's the perimeter?
Dialogue: 0,0:05:55.26,0:05:58.66,Default,,0000,0000,0000,,Well, it's going to be equal to\Nthis distance down here, which
Dialogue: 0,0:05:58.66,0:06:03.67,Default,,0000,0000,0000,,is 7 centimeters, plus this\Ndistance over here which is 4
Dialogue: 0,0:06:03.67,0:06:07.48,Default,,0000,0000,0000,,centimeters, plus the distance\Non the top -- this is a
Dialogue: 0,0:06:07.48,0:06:09.17,Default,,0000,0000,0000,,rectangle, it's going to be\Nthe same distance as
Dialogue: 0,0:06:09.17,0:06:10.44,Default,,0000,0000,0000,,this one over here.
Dialogue: 0,0:06:10.44,0:06:13.17,Default,,0000,0000,0000,,So plus another 7 centimeters.
Dialogue: 0,0:06:13.17,0:06:16.30,Default,,0000,0000,0000,,Then you're going to have this\Ndistance on the left hand side.
Dialogue: 0,0:06:16.30,0:06:18.87,Default,,0000,0000,0000,,But this distance on the left\Nhand side is the same as this
Dialogue: 0,0:06:18.87,0:06:21.81,Default,,0000,0000,0000,,distance right here -- this\Nis also 4 centimeters.
Dialogue: 0,0:06:21.81,0:06:24.45,Default,,0000,0000,0000,,So plus another 4 centimeters.
Dialogue: 0,0:06:24.45,0:06:25.45,Default,,0000,0000,0000,,And what do you get?
Dialogue: 0,0:06:25.45,0:06:27.57,Default,,0000,0000,0000,,You get 7 plus 4 which is\N11, and then you have
Dialogue: 0,0:06:27.57,0:06:29.02,Default,,0000,0000,0000,,another 7 plus 4.
Dialogue: 0,0:06:29.02,0:06:33.02,Default,,0000,0000,0000,,You have 11 plus 11, so\Nyou have 22 centimeters.
Dialogue: 0,0:06:33.02,0:06:36.30,Default,,0000,0000,0000,,Once again, it's not\Na square centimeter.
Dialogue: 0,0:06:36.30,0:06:42.30,Default,,0000,0000,0000,,Now let's divert -- let's go\Naway from our rectangle analogy
Dialogue: 0,0:06:42.30,0:06:43.76,Default,,0000,0000,0000,,or our rectangle examples.
Dialogue: 0,0:06:43.76,0:06:46.93,Default,,0000,0000,0000,,So let's see if we can do\Nthe same with triangles.
Dialogue: 0,0:06:46.93,0:06:49.94,Default,,0000,0000,0000,,So let's say I have\Na triangle here.
Dialogue: 0,0:06:49.94,0:06:52.10,Default,,0000,0000,0000,,I have a triangle like this.
Dialogue: 0,0:06:54.99,0:06:58.72,Default,,0000,0000,0000,,Let's say that this distance\Nright here -- actually
Dialogue: 0,0:06:58.72,0:06:59.76,Default,,0000,0000,0000,,let me draw it like this.
Dialogue: 0,0:06:59.76,0:07:02.21,Default,,0000,0000,0000,,I think this'll make it a\Nlittle bit easier for you
Dialogue: 0,0:07:02.21,0:07:04.55,Default,,0000,0000,0000,,to see how this relates\Nto a rectangle.
Dialogue: 0,0:07:04.55,0:07:05.81,Default,,0000,0000,0000,,Let me draw it like this.
Dialogue: 0,0:07:09.36,0:07:09.81,Default,,0000,0000,0000,,There you go.
Dialogue: 0,0:07:09.81,0:07:11.30,Default,,0000,0000,0000,,That's my triangle.
Dialogue: 0,0:07:11.30,0:07:14.51,Default,,0000,0000,0000,,And let's say that this\Ndistance right here is 7
Dialogue: 0,0:07:14.51,0:07:17.21,Default,,0000,0000,0000,,centimeters right down there.
Dialogue: 0,0:07:17.21,0:07:21.09,Default,,0000,0000,0000,,And let's say that the\Nheight of this triangle
Dialogue: 0,0:07:21.09,0:07:23.52,Default,,0000,0000,0000,,is 4 centimeters.
Dialogue: 0,0:07:23.52,0:07:26.16,Default,,0000,0000,0000,,And I were to ask you what is\Nthe area of the triangle?
Dialogue: 0,0:07:33.69,0:07:36.59,Default,,0000,0000,0000,,Well, when we had a rectangle\Nlike this, we just
Dialogue: 0,0:07:36.59,0:07:38.66,Default,,0000,0000,0000,,multiplied 7 times 4.
Dialogue: 0,0:07:38.66,0:07:39.60,Default,,0000,0000,0000,,But what would that give us?
Dialogue: 0,0:07:39.60,0:07:42.61,Default,,0000,0000,0000,,That would give us the area\Nof an entire rectangle.
Dialogue: 0,0:07:42.61,0:07:44.61,Default,,0000,0000,0000,,If we did 7 times 4, that\Nwould give us the area of
Dialogue: 0,0:07:44.61,0:07:46.05,Default,,0000,0000,0000,,this entire rectangle.
Dialogue: 0,0:07:46.05,0:07:49.64,Default,,0000,0000,0000,,You could imagine extending\Nmy triangle up like this.
Dialogue: 0,0:07:49.64,0:07:51.88,Default,,0000,0000,0000,,This is a right triangle --\Nthis is going straight up and
Dialogue: 0,0:07:51.88,0:07:54.42,Default,,0000,0000,0000,,down, this is going straight\Nleft and right on the
Dialogue: 0,0:07:54.42,0:07:55.91,Default,,0000,0000,0000,,bottom right here.
Dialogue: 0,0:07:55.91,0:07:58.91,Default,,0000,0000,0000,,It's a 90 degree angle, if\Nyou've been exposed to the
Dialogue: 0,0:07:58.91,0:08:00.04,Default,,0000,0000,0000,,idea of angles already.
Dialogue: 0,0:08:00.04,0:08:03.46,Default,,0000,0000,0000,,So you could almost view it as\Nit's 1/2 of this rectangle.
Dialogue: 0,0:08:03.46,0:08:04.61,Default,,0000,0000,0000,,Not really almost, it is.
Dialogue: 0,0:08:04.61,0:08:07.58,Default,,0000,0000,0000,,Because if you just double this\Nguy, you could imagine if you
Dialogue: 0,0:08:07.58,0:08:12.19,Default,,0000,0000,0000,,flip this triangle over, you\Nget the same triangle but
Dialogue: 0,0:08:12.19,0:08:14.91,Default,,0000,0000,0000,,it's just upside down\Nand flipped over.
Dialogue: 0,0:08:14.91,0:08:17.65,Default,,0000,0000,0000,,So if you think about when you\Nmultiply 7 times 4, you're
Dialogue: 0,0:08:17.65,0:08:25.14,Default,,0000,0000,0000,,getting the area of this entire\Nrectangle, which we
Dialogue: 0,0:08:25.14,0:08:26.80,Default,,0000,0000,0000,,just did up here.
Dialogue: 0,0:08:26.80,0:08:30.21,Default,,0000,0000,0000,,But we want to know the\Narea of the triangle.
Dialogue: 0,0:08:30.21,0:08:33.19,Default,,0000,0000,0000,,We want to know just\Nthis area right here.
Dialogue: 0,0:08:33.19,0:08:36.29,Default,,0000,0000,0000,,You can see, hopefully, from\Nthis drawing that the area of
Dialogue: 0,0:08:36.29,0:08:39.39,Default,,0000,0000,0000,,this triangle is exactly 1/2\Nof the area of the
Dialogue: 0,0:08:39.39,0:08:40.99,Default,,0000,0000,0000,,entire rectangle.
Dialogue: 0,0:08:40.99,0:08:47.04,Default,,0000,0000,0000,,So the area for a triangle is\Nequal to the base times the
Dialogue: 0,0:08:47.04,0:08:50.49,Default,,0000,0000,0000,,height -- now this so far,\Nbase times height is the
Dialogue: 0,0:08:50.49,0:08:52.15,Default,,0000,0000,0000,,area of a rectangle.
Dialogue: 0,0:08:52.15,0:08:53.76,Default,,0000,0000,0000,,So in order to get the area of\Nthe triangle, you're going
Dialogue: 0,0:08:53.76,0:08:55.91,Default,,0000,0000,0000,,to multiply that times 1/2.
Dialogue: 0,0:08:55.91,0:08:58.16,Default,,0000,0000,0000,,So 1/2 base times height.
Dialogue: 0,0:08:58.16,0:09:04.32,Default,,0000,0000,0000,,So in our example it's going\Nto be 1/2 times 7 centimeters
Dialogue: 0,0:09:04.32,0:09:07.02,Default,,0000,0000,0000,,times 4 centimeters.
Dialogue: 0,0:09:07.02,0:09:10.78,Default,,0000,0000,0000,,We know what 7 times 4 is.
Dialogue: 0,0:09:10.78,0:09:13.88,Default,,0000,0000,0000,,We already know it's\N28 centimeters -- we
Dialogue: 0,0:09:13.88,0:09:15.71,Default,,0000,0000,0000,,did that up there.
Dialogue: 0,0:09:15.71,0:09:19.05,Default,,0000,0000,0000,,So this right here\Nis 28 centimeters.
Dialogue: 0,0:09:19.05,0:09:22.07,Default,,0000,0000,0000,,Then we want centimeters and we\Nwant to multiply that by 1/2.
Dialogue: 0,0:09:22.07,0:09:26.72,Default,,0000,0000,0000,,So that's going to be 14\Ncentimeters just like that.
Dialogue: 0,0:09:26.72,0:09:29.95,Default,,0000,0000,0000,,So the area of this triangle\Nis exactly 1/2 of the
Dialogue: 0,0:09:29.95,0:09:31.70,Default,,0000,0000,0000,,area of that rectangle.
Dialogue: 0,0:09:31.70,0:09:35.67,Default,,0000,0000,0000,,Now, the perimeter of this\Ntriangle becomes a little bit
Dialogue: 0,0:09:35.67,0:09:43.38,Default,,0000,0000,0000,,more complicated because\Nfiguring out this distance
Dialogue: 0,0:09:43.38,0:09:45.32,Default,,0000,0000,0000,,isn't the easiest\Nthing in the world.
Dialogue: 0,0:09:45.32,0:09:47.96,Default,,0000,0000,0000,,Well, it will be easy for\Nyou once you get exposed to
Dialogue: 0,0:09:47.96,0:09:48.87,Default,,0000,0000,0000,,the Pythagorean Theorem.
Dialogue: 0,0:09:48.87,0:09:50.29,Default,,0000,0000,0000,,But I'm going to skip\Nthat right now.
Dialogue: 0,0:09:50.29,0:09:54.01,Default,,0000,0000,0000,,I'm going to leave that for the\NPythagorean Theorem video.
Dialogue: 0,0:09:54.01,0:09:58.45,Default,,0000,0000,0000,,Let me just give you one\Nmore area of a triangle.
Dialogue: 0,0:09:58.45,0:10:00.12,Default,,0000,0000,0000,,Let's say I have a triangle\Nthat looks like this.
Dialogue: 0,0:10:00.12,0:10:03.19,Default,,0000,0000,0000,,This was a very special case\Nthat I drew to make it look
Dialogue: 0,0:10:03.19,0:10:04.52,Default,,0000,0000,0000,,like half of a rectangle.
Dialogue: 0,0:10:04.52,0:10:07.22,Default,,0000,0000,0000,,Let's say we had a triangle\Nthat looks like this.
Dialogue: 0,0:10:07.22,0:10:11.65,Default,,0000,0000,0000,,It's a little bit more\Nskewed looking like this.
Dialogue: 0,0:10:11.65,0:10:19.35,Default,,0000,0000,0000,,And let's say that this\Ndistance down here is 3 meters
Dialogue: 0,0:10:19.35,0:10:21.95,Default,,0000,0000,0000,,-- that distance is 3 meters.
Dialogue: 0,0:10:21.95,0:10:25.23,Default,,0000,0000,0000,,Let's say we don't know what\Nthat distance is and we don't
Dialogue: 0,0:10:25.23,0:10:26.57,Default,,0000,0000,0000,,know what that distance is.
Dialogue: 0,0:10:26.57,0:10:30.66,Default,,0000,0000,0000,,But we do know that if we were\Nto kind of drop a line straight
Dialogue: 0,0:10:30.66,0:10:32.67,Default,,0000,0000,0000,,down like this -- if you\Nimagine this was a building or
Dialogue: 0,0:10:32.67,0:10:34.76,Default,,0000,0000,0000,,some type of mountain and you\Njust drop something straight
Dialogue: 0,0:10:34.76,0:10:38.85,Default,,0000,0000,0000,,down onto the ground like that,\Nwe know that this distance
Dialogue: 0,0:10:38.85,0:10:43.77,Default,,0000,0000,0000,,is equal to -- let's say\Nit's equal to 4 meters.
Dialogue: 0,0:10:43.77,0:10:46.14,Default,,0000,0000,0000,,So what is the area of this\Ntriangle going to be?
Dialogue: 0,0:10:50.42,0:10:52.91,Default,,0000,0000,0000,,Well, we apply the\Nsame formula.
Dialogue: 0,0:10:52.91,0:10:57.17,Default,,0000,0000,0000,,Area is equal to 1/2\Nbase times height.
Dialogue: 0,0:10:57.17,0:11:00.49,Default,,0000,0000,0000,,So it's equal to 1/2 -- the\Nbase is literally this base
Dialogue: 0,0:11:00.49,0:11:02.26,Default,,0000,0000,0000,,right here of this triangle.
Dialogue: 0,0:11:02.26,0:11:07.38,Default,,0000,0000,0000,,So 1/2 times 3 times the\Nheight of the triangle.
Dialogue: 0,0:11:07.38,0:11:08.74,Default,,0000,0000,0000,,I guess a better way\Nto think of it is an
Dialogue: 0,0:11:08.74,0:11:10.57,Default,,0000,0000,0000,,altitude of the triangle.
Dialogue: 0,0:11:10.57,0:11:12.76,Default,,0000,0000,0000,,So this thing isn't even in\Nthe triangle, but it is
Dialogue: 0,0:11:12.76,0:11:13.82,Default,,0000,0000,0000,,literally the height.
Dialogue: 0,0:11:13.82,0:11:15.85,Default,,0000,0000,0000,,If you imagine this was a\Nbuilding, you say how high is
Dialogue: 0,0:11:15.85,0:11:18.36,Default,,0000,0000,0000,,the building, it would be\Nthis height right there.
Dialogue: 0,0:11:18.36,0:11:20.40,Default,,0000,0000,0000,,So 1/2 times 3 times 4.
Dialogue: 0,0:11:20.40,0:11:22.88,Default,,0000,0000,0000,,You use that distance\Nright there.
Dialogue: 0,0:11:22.88,0:11:27.86,Default,,0000,0000,0000,,Which is equal to 3 times 4 is\N12 times 1/2 is equal to 6.
Dialogue: 0,0:11:27.86,0:11:30.83,Default,,0000,0000,0000,,We're going to be dealing\Nwith square meters.
Dialogue: 0,0:11:30.83,0:11:34.14,Default,,0000,0000,0000,,I really want to highlight the\Nidea, because if I gave you a
Dialogue: 0,0:11:34.14,0:11:40.00,Default,,0000,0000,0000,,triangle that looked like this,\Nwhere if this was 3 meters down
Dialogue: 0,0:11:40.00,0:11:44.25,Default,,0000,0000,0000,,here, and then if I were to\Ntell you that this side over
Dialogue: 0,0:11:44.25,0:11:50.93,Default,,0000,0000,0000,,here is 4 meters, this is not\Nsomething that you can just
Dialogue: 0,0:11:50.93,0:11:52.82,Default,,0000,0000,0000,,apply this formula\Nto and figure out.
Dialogue: 0,0:11:52.82,0:11:54.79,Default,,0000,0000,0000,,In fact, you'd have to know\Nsome of the angles and whatnot
Dialogue: 0,0:11:54.79,0:11:56.84,Default,,0000,0000,0000,,to really be able to figure out\Nthe area, or you'd have to
Dialogue: 0,0:11:56.84,0:11:58.35,Default,,0000,0000,0000,,know this other side here.
Dialogue: 0,0:11:58.35,0:12:02.48,Default,,0000,0000,0000,,So this is not easy.
Dialogue: 0,0:12:02.48,0:12:05.89,Default,,0000,0000,0000,,You have to know what the\Naltitude or the height
Dialogue: 0,0:12:05.89,0:12:06.72,Default,,0000,0000,0000,,of the triangle is.
Dialogue: 0,0:12:06.72,0:12:07.90,Default,,0000,0000,0000,,You need to know this distance.
Dialogue: 0,0:12:07.90,0:12:11.33,Default,,0000,0000,0000,,In this case, it was one of\Nthe sides, but in this case
Dialogue: 0,0:12:11.33,0:12:12.29,Default,,0000,0000,0000,,it's not one of the sides.
Dialogue: 0,0:12:12.29,0:12:15.84,Default,,0000,0000,0000,,You'd have to figure out what\Nthat side right there on the
Dialogue: 0,0:12:15.84,0:12:19.59,Default,,0000,0000,0000,,right hand side is in order\Nto apply this formula.