Area of composite or compound shapes - fast math lesson - Free Educational videos for Students in K-12

Area of composite or compound shapes - fast math lesson - By tecmath

Transcript


00:0-1	good and welcome to take mouth channel what we're gonna
00:02	be having a look at this video is how to
00:03	work out the area of composite shapes . Now ,
00:06	I would expect . Already they're gonna have some basis
00:08	in working out area of what area actually is areas
00:12	of space bound within a two dimensional shape . We've
00:15	looked at these in some earlier videos and a composite
00:18	shapes , literally just a shape That's made up of
00:20	two or more regular shapes . Okay , so I'll
00:23	give you some examples about three examples on different types
00:28	of shapes that you might get and how you might
00:30	solve them . Okay , so first off , I'll
00:32	draw a type of composite shape and one you might
00:36	see might look like this . Okay , so it's
00:39	not a standard sort of shape that might look like
00:42	this . Okay , I'll try to be date when
00:47	I'm doing these . Okay , so this is not
00:53	a standard sort of shape . It's an irregular sort
00:56	of shape . It's made up of different sizes now
00:59	. What about straight away ? I will on the
01:02	different sizes on this . So first off , let's
01:05	make this one here . four cm . This site
01:10	here is also going to be 4cm if that's the
01:13	case , this is four . And this is for
01:15	it's gonna make this side here . eight cm .
01:18	You see that ? Uh we also have a side
01:21	here which I'm going to make six centimeters . We
01:26	have a site here which I'm going to make five
01:29	centimeters And it means that this site here would have
01:33	to be one cm . Okay , because 5-plus 1
01:38	is six . Then how do we work out the
01:40	area of this compensate shape ? Well , it's really
01:43	, really simple . We literally just cut it up
01:45	into the regular shapes , which it's made . Okay
01:48	, so I'll show you how to do this in
01:50	a nice color here and I think it's going to
01:52	cut it now , look , it doesn't matter if
01:53	you cut it here or here , but I'm going
01:55	to cut it here . So what I've got now
02:00	is a shape like this in the shape on this
02:05	. So first off , I'm gonna look at this
02:07	shape here , then I'm gonna look at this shape
02:10	here . So let's write down there formula for area
02:14	, area equals Length , times width . And that's
02:18	for rectangle . So it's gonna be like this for
02:21	both of these shapes . So for the area for
02:23	part one is as follows , we need a length
02:26	that we need . Now . The easiest way to
02:28	do this , I find on a two dimensional shape
02:31	, like a rectangle is to go to the corner
02:34	. Okay , so quarter just here and you'll see
02:37	that go up this way , we have five centimeters
02:44	and going this way We have four cm . And
02:50	the only reason I do this is because people sometimes
02:53	get stuck about which ones are multiplied . So we
02:55	can go to the corner about two dimensional shape .
02:57	We can head off in this direction and this direction
02:59	it tells us our length and are with the major
03:01	one is also make sure that you know you're not
03:03	starting here and going all the way across , you're
03:06	only going to hear . So five times 45 centimeters
03:10	times four centimeters . The area shaped wound , he's
03:14	going to be 20 centimetres squid . Okay , what
03:20	about the area of shape two . So we're gonna
03:27	need a length in the week . So a leak
03:30	of the start here . We have six sevens .
03:36	Mhm . And I'm gonna be times in this by
03:42	this word from here to hear Which is not 8cm
03:47	somewhat . Go down here and see what it is
03:48	. It's four cm the six by four centimeters .
03:55	Okay , so be very careful that you don't read
03:57	this number here . It's actually this with six times
04:01	four equals 24 centimetres squared . So we have as
04:09	you see . Yeah . And here are two areas
04:16	And I want to know what they are together .
04:17	Okay , so 20 plus 24 . So we have
04:21	a total area . Total area which I was going
04:23	to put down his ta equals 20 plus 24 ,
04:28	which is 40 four centimeters square . Okay , so
04:34	that's one way you might work these out again .
04:36	Just a couple of things to be careful of .
04:38	Is that you don't go too far on these ?
04:39	You are really the right measurements . Okay . Yeah
04:45	. What about I go and we have a look
04:46	at a different example here . Let's have a look
04:50	at one . Say where we have . Okay ,
04:54	I'll do a rectangular type one again and then I'm
04:56	going to ones involving try and get the type stuff
04:59	. So what about we do this sort of shape
05:02	here ? Like I just so we get this sort
05:14	of shape and I'll put some sizes on it .
05:17	This year . I'm going to say is 17 cm
05:21	. This year is 16 centimeters . Uh This one
05:28	here is uh mhm . 13 cm . And this
05:35	one here is , what about we call this one
05:38	? 14 celebrators . Okay . Could you work at
05:43	the area of this ? First off , you're going
05:45	to notice that we have some unknown side . So
05:48	it's really good policy straight away , is to work
05:50	these out . So is this a 16 ? And
05:53	this is 13 ? This side and this side would
05:55	have to add up 16 . 13 plus what equals
05:58	16 . This one here is going to be three
06:01	centimeters . This one here , 17 . Take a
06:06	way forward for 14 plus this one in 17 .
06:09	This one here is also going to be three centimeters
06:14	. Okay . In fact , I might even move
06:17	these in a second just to help us out .
06:20	So actually the easiest way of working this out is
06:23	kind of strange ways to get rid of these .
06:25	It has to move them inside a square here .
06:28	You'll see what I'm gonna do . What I'm gonna
06:31	do is I'm actually gonna pretend well we have an
06:34	entire box here and I'm gonna work in the area
06:37	and they're not gonna take this little box away .
06:40	And that will give us a total sort of the
06:42	total area . Yeah , so let's do that .
06:45	So first off we have uh yeah , part one
06:50	hand . And we're gonna be taking away area too
06:55	. Okay , so area equals length . Let's put
07:00	the format in first . So the area of part
07:06	one equals 16 centimeters 16 centimeters By 17cm . Have
07:19	gone from that corn and 16cm 78 centimeters . We're
07:24	going to be times in these together . So 16
07:27	cm time 17cm . The answer to that is 270
07:34	two centimeters squid . Okay , pretty easy . So
07:40	far . What about we work at the area of
07:44	# 2 ? This area of part two here and
07:48	the area of that is three cm times three cm
07:52	. 3 cm times three centimeters equals no it's celebrators
08:01	squared . So now we're almost done . A total
08:05	area is the same as this one . Take away
08:12	this one . Okay , the same as this one
08:15	. Take away this little one here , we're getting
08:17	rid of it . Okay , so the total area
08:20	20 270 to take away nine . So what does
08:24	that they call ? 272 celebrated swear . Take away
08:31	dying centimeters squared equals 260 three centimetres squid . Okay
08:46	, what about one last one of these ? Hopefully
08:48	you're feeling really confident with these . Okay . Um
08:54	I might even go something a little bit ridiculous now
08:56	but it will probably be the hardest one . Type
08:58	of one that you would get . Okay . And
09:00	I think we should probably do that to say we
09:04	had a shape that look line this councilor little house
09:15	and what we're going to do actually , he's in
09:20	this house on the draw the door that you're taking
09:25	out . How horrible is that ? Okay , so
09:30	what we're gonna do is I'm gonna give you a
09:32	couple of vital measurements that you do need . Okay
09:36	, so first off we have this length here which
09:39	is going to be six cm . We're going to
09:44	have this one here which is going to be two
09:47	centimeters . This one here , I'm gonna mark as
09:50	being two cm . This one here is 2cm As
09:54	well as these ones . That line there means they're
09:56	all two cm . Okay . The only other thing
10:00	I need is a height here to do and I'll
10:04	actually do it with a line going across here and
10:07	their height can be . What about we call that
10:13	? Three centimeters ? Okay . So how can we
10:20	attack this one ? How can we work at the
10:21	area of this particular shape ? You can cut it
10:25	up . But I think the easiest way to say
10:26	we worked at the area of this triangle . Okay
10:29	, so we'll do that first . Will work at
10:30	the area of the triangle . They will work at
10:34	the area of a box here and we're gonna take
10:39	it this area . Yeah . Okay , so let's
10:43	do this . First off the area . We've got
10:46	two areas we're dealing with an area of a triangle
10:49	. This area of the triangle equals remember , half
10:53	the base times the heart . This equals the basic
11:00	idea is two plus two plus two is the base
11:04	. So that's six . A half of the base
11:07	Is three . It's the half of 6 1st six
11:11	centimeters Times the height , which is three cm .
11:17	So this is equal to three centimeters times three centimeters
11:24	. This is equal 29 cm two . And I
11:30	want to put the triangle shape there so I can
11:33	remember which one I'm dealing with the area . The
11:37	other ones areas equal length times with this is gonna
11:43	be for our Square . This is our number one
11:46	here . This is going to be for two in
11:49	for three . Okay , so the area of this
11:56	one here this equals the length which again I go
12:00	to a corner here . So customized . Go from
12:02	this one . We have a length which is all
12:04	the way across here which is six centimetres . That's
12:09	two plus two plus two . And we're gonna time
12:11	just by 66cm . Time . six cm equals 36
12:20	cm squared Area . Part three . The bit we're
12:26	taking away . So we're gonna put these two together
12:30	. Uh and then we're gonna take this little bit
12:32	away . It's the area . This little one is
12:35	two centimeters times two centimeters . It's not two plus
12:38	two plus two which I've had people in my class
12:41	there before . It's two times two is a length
12:44	top of the window . So this one equal two
12:48	centimeters times two centimeters vehicles , four centimeters squared now
12:57	that we've got all the numbers there . And what
12:58	are we doing with them ? We're getting this number
13:00	here . So this one here , we're adding it
13:02	to this number here and we're taking away the sort
13:04	of one . So this one plus this one .
13:06	Take this one . So our total area Is as
13:11	follows . nine plus 36 Is 45 take away four
13:16	, his 41 cm squared . I kind hopefully that
13:23	was some help of you there and you can understand
13:26	how we're going about that . And hopefully they're all
13:30	good answers anyway . See you next time , boy
00:0-1	.

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