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

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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