Area of rectangles and triangles - fast math lesson! - Free Educational videos for Students in K-12

Area of rectangles and triangles - fast math lesson! - By tecmath

Transcript


00:0-1	Good day and welcome to the Tech Math channel .
00:01	We're gonna be able to look at in this video
00:03	is how to work out area . Um So first
00:06	off we're gonna have a look at the units of
00:07	area . So area . Pretty much I'll write that
00:10	word up . Their area is basically the part of
00:16	the surface that is inside a boundary . So I'll
00:18	give you an example uh it's it's in a two
00:21	dimensional sort of thing . So first off I think
00:23	it's really important to get this idea of dimensions .
00:25	So we have one dimensional one day we have to
00:29	d and we have 32 Yeah . Look I think
00:33	a lot of people don't work uh 32 years because
00:37	we'll get to that in a second because three D
00:38	. Tv . But one dimension is where we just
00:41	have to say something like that . Two dimensions is
00:44	where we have say length and width . So an
00:47	object that is flat is said to be two dimensional
00:50	. When you look at the television And not a
00:52	3D TV . That's two dimensions or a picture .
00:55	Okay . It has a length and it has a
00:57	width But a 3D shape has length a week .
01:07	And maybe a depth you want to call it .
01:09	Okay so length but we've and a depth that has
01:12	three dimensions . Okay this is what it's called .
01:16	Three dimensions . So with area , the one we're
01:20	looking at is we're looking at two dimensional shapes .
01:24	Okay so let's get rid of these other two .
01:26	So we'll be looking at two D shapes when we're
01:29	looking at area . Yeah I just want to get
01:32	into the units that we use when we look at
01:34	two D shapes . So first off we might use
01:37	for really small areas . We might you say something
01:39	like square millimeters . So we measure area in squares
01:44	. So for example we might have a shape like
01:48	this . We want to know how big it is
01:50	we get . So maybe this thing here is four
01:55	cm this year is three cm . And so I
02:00	could mark them 1234 and this is 123 They would've
02:04	cut these up . You would see I've cut them
02:08	up four times this way . And three times this
02:10	way . We end up with 123456789 10 , 11
02:15	, 12 of these squares . Okay , these squares
02:23	basically how we measure two dimensional shapes . Okay ,
02:27	so for really , really small shapes , we might
02:29	use something like millimeters squared . We write that like
02:34	this millimeters square . Or we might even call it
02:36	square millimeters . Uh say something like the area of
02:40	a postage stamp . Okay , so say this was
02:43	a postage stamp , We would probably use square millimeters
02:49	. Okay , uh so we were working out say
02:53	something like the area of your computer screen here ,
02:56	which is measured probably get measured across and centimeters and
02:59	centimeters . We would actually end up using say something
03:02	a bit different , which is square centimeters . Uh
03:07	but a lot of time what we actually use a
03:09	look at the floor around you and that , which
03:11	is measured more in meters , meters . About a
03:13	fairly decent sized step . We actually measure so the
03:17	classroom or the room you're in right now in square
03:20	meters . Okay . Often when they talk about sally
03:24	selling houses , they talk about square meters and they
03:27	confuse these with buildings , squares which are something slightly
03:30	different . Um and then if you get into really
03:33	, really big things to say , we're talking about
03:35	the area of a an ocean or or a big
03:38	park or something , we might even talk about this
03:40	in terms of square kilometers . Okay . But the
03:44	idea that you have to get with these is that
03:46	they're this sort of shape . So this would be
03:48	like if it's a square centimeter , it would be
03:53	quite literally a centimeter by a centimeter or it was
03:59	a square meter . It would be a meter by
04:02	a meter . Okay , So you can actually imagine
04:04	a meter this way , in a better that way
04:07	. And that was what we'd call a meta square
04:10	and that's how we measure two dimensional objects . So
04:15	let's have a look at this and let's work out
04:19	how to work out area two area . He's worked
04:24	at his followers to work at the area of a
04:27	rectangle was fairly easy or rectangle or a square .
04:31	The way we do this is as follows . So
04:33	, so this here was four cm and this one
04:37	here is three cm . The way that we work
04:41	at the area of a standard rectangle or a square
04:44	is just length times week . Okay , so this
04:50	was the area equals this . So we would call
04:53	this . So the length here is 4cm Times the
04:57	width , which is three cm . So all of
05:01	this would equal . So here's 1234 and here's 123
05:06	We'll end up with 123456789 10 , 11 , 12
05:11	centimeters , squeeze . So that's the way we work
05:15	at the area of a rectangle . We're gonna have
05:17	a look at rectangles , we're gonna look at triangles
05:20	and we're also going to look at these things which
05:22	are more complex shapes in a different video . So
05:25	I look at triangles in this video . Um so
05:28	say we wanted to work out the area of a
05:31	different rectangle . I'll get you to work this one
05:33	out and then we'll go to the areas and triangles
05:37	to say I want you to work at the area
05:40	of this , recommended it measures uh three m .
05:50	Bye . For 25 m . Okay , how would
05:58	you work this out ? This is a panacea .
06:00	Alright , because what I've actually done is I've given
06:03	you a half meter here , but the idea is
06:05	the same area eagles like for a tweet to this
06:10	equals The length , which is 4.5 m . It's
06:16	all of the week , Which is three letters ,
06:20	So 4.5 times three . And what's the answer to
06:24	that ? The answer that is 13.5 meters squared .
06:31	Okay . What about I get you working at the
06:33	area of a triangle ? Because rectangles as you probably
06:36	agree . Now , really really easy to work out
06:38	. What about I get you working at the area
06:40	of a triangle ? So let's do that right now
06:43	, but it right , the restaurant area here .
06:45	Um So a triangle . Um they're gonna give you
06:49	a bit of a hit with this , I'm gonna
06:53	give you a length . Which is a What about
06:58	I go uh five cm and this one can be
07:02	four cm . Okay how did you work at the
07:06	area of this ? Now ? You're gonna see we
07:08	go length by width . What that would actually work
07:10	out is not this triangle , It would actually work
07:13	out a rectangle . That was this show . That
07:16	is the worst square I have ever drawn . The
07:19	worst rectangle but working out a rectangle which was this
07:23	show . Okay , correct . And we did that
07:27	, let's do that . We weren't lengthwise with We
07:30	would get the answer of five times for which would
07:34	equal 20 centimeters squared . But you're gonna notice we're
07:39	not doing half , we're not doing the whole of
07:42	this rectangle , We're actually doing half of it .
07:45	Okay So what do we do ? We actually have
07:49	our answer . So this divided by two equals 10
07:54	centimetres square . And this is the reason often when
07:56	you hear about people talking about triangles and the area
08:00	of them , they give you this formula instead ,
08:03	which is um you might see it written down and
08:08	say not length times with but half length times with
08:12	quite commonly . You also see this written is half
08:15	base times height , but it's pretty much the same
08:18	thing . Okay , so let's use this particular formula
08:23	to work out the area of this triangle here .
08:28	So if we do this triangle here , we need
08:30	a couple of things . What we need is we
08:32	need a base . Okay Which is this distance here
08:37	? So suddenly call this 10 centimetres . We also
08:42	need a heart which is a this bit here .
08:48	Okay , so call this 8cm . Okay , the
08:52	heights of this distance here is not this distance here
08:54	. Heidi is this distance here ? And you might
08:57	see that this is actually half a rectangle . It
09:00	would be this sort of shape . You might even
09:02	want to draw it around . In fact , I'll
09:03	do that . I'll draw this rectangle around . Okay
09:10	. You won't see this big matches , this bit
09:13	in this big matches this week . So it does
09:14	actually work . So , let's work at the area
09:16	here . This area equals half length times with vehicles
09:22	. Uh huh . Of the length , which is
09:25	the half of 10 times a week . Which types
09:30	of heart or half the length tubs of with or
09:34	a half of 10 times eight . Uh In fact
09:38	, I might even changes . Look as long as
09:40	you're having one of these answers , it actually doesn't
09:42	matter . So I take that as technical as I'm
09:45	doing the length , I probably should do it .
09:47	Well , which one ? So let's do this .
09:50	Half the base times height . Maybe that's a nicer
09:55	way of saying , Okay , so half of the
09:58	base is half of 10 times higher , which is
10:01	Okay , but you're gonna see the formula is much
10:04	the same and it doesn't matter if you were to
10:06	work at half of eight and times it by 10
10:08	, it's gonna be the same as having 10 times
10:10	by eight . So half of 10 , it's five
10:13	times eight and these are both in centimeters . This
10:17	is if I could actually write this , This is
10:21	actually five cm times eight centimeters and this equals 40
10:29	cm . There's too lots of them . It's weird
10:33	. Okay , and that's the area of a triangle
10:36	there . So that's the way we go about working
10:38	out areas . Hopefully you're pretty good with those .
10:41	Anyway , So the next one

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