Find the Area of Composite Shapes Easily - How to work out the Area of ANY Composite Figure. - Free Educational videos for Students in K-12

Find the Area of Composite Shapes Easily - How to work out the Area of ANY Composite Figure. - By tecmath

Transcript


00:0-1	Good day . Welcome to Tech Math channel . I'm
00:01	josh . What we're going to be having a look
00:03	at in this video is how to work out the
00:05	area of composite shapes . That is the area within
00:07	each of these shapes here . And as you can
00:09	see they contain things like rectangles as well as triangles
00:13	as well as circles . So I've got a whole
00:15	variety of these here to show now the way that
00:18	we do these , the steps are pretty much the
00:20	same that I'd recommend each time and I've put these
00:22	out over here . So the first thing that you
00:25	want to do is when we work this out ,
00:27	the first thing we're going to do is we're gonna
00:29	put the measurements into the same base units , but
00:32	also the required based units . What I mean by
00:34	this say that you actually worked at the end of
00:36	the floor . You wouldn't want to work it out
00:38	in square millimeters or square inches because these wouldn't be
00:42	a useful measurement . You've been wanting to work out
00:45	things in square meters . So first off , you
00:47	put the measurements into those units that you require them
00:49	to be in and also they're going to be the
00:51	same base units . Then what we're gonna do is
00:54	we're gonna break these into simpler shapes . As you
00:57	can see here . We might break this rectangle here
00:59	, the shape here into a rectangle and a semicircle
01:03	. Or maybe we break this into some rectangles here
01:05	. We're going to work out the area of these
01:07	simpler shapes and then do a bit of addition subtraction
01:11	finally to work out the total area . Okay ,
01:14	so let's go through and do this . We're going
01:16	to follow the same steps every time if you do
01:18	this , you won't go too badly . So let's
01:21	get right into this . Okay , to our first
01:23	example , we have this L shape here and we're
01:25	going to work out the area within it . So
01:27	let's go to step one here , we're going to
01:29	put the measurements into the required or the same base
01:33	units . Now , centimeters is okay , we haven't
01:35	got any specific units , we have to put them
01:37	in and we're gonna also notice that they're all in
01:39	centimeters . So this step is already done . We
01:42	only have to change if there was different units or
01:44	we say we want them in different units and we'll
01:46	see an example that a bit later on . The
01:48	next thing we're going to do is we're going to
01:50	break these into simpler shapes . Now , just a
01:52	word of caution here because I have seen students do
01:55	this a lot , they're going to break this shape
01:57	into two separate shapes and they put a line right
02:00	here . Now this is not going to make it
02:03	into a simpler shape . Now you're left with this
02:05	shape and this shape , neither of which are easier
02:07	to work out the actual area for . This is
02:10	not the type of shape we're looking at , we're
02:11	looking at simpler shapes , shapes like rectangles , triangles
02:14	, circles , even semi circles . We're going to
02:17	break this into two rectangles . So we're putting a
02:20	line here . We could have also put one here
02:22	. We only need to put one line here ,
02:24	we've broken into one rectangle here and another rectangle here
02:28	. So now let's work out the area of these
02:30	simplest shapes . We have two rectangles . We have
02:33	this rectangle here , we'll call rectangle one . And
02:35	this rectangle here , we'll call Rectangle too . So
02:39	first for rectangle one . Okay , so area is
02:43	equal to length times . With so what's the length
02:47	of this particular rectangle ? You can see that it's
02:49	6cm . We're going to multiply that by the width
02:54	. And what's the width of this ? It's four
02:55	centimeters So six centimetres by four centimeters we have area
03:00	one which is six fours 24 . And this is
03:04	going to be an answer in centimeters squared , a
03:08	centimeter squared literally . We have 24 of these cm
03:12	where you don't believe you can go through and count
03:14	them . So now let's work out the area of
03:17	a rectangle to here . So like all rectangles ,
03:20	the area is equal to the length , times the
03:23	width . Okay , so let's treat one side like
03:26	the length and the other side like the width .
03:27	And we'll go from there . So this length here
03:30	we'll call that the length . So how long is
03:33	that ? You're gonna see that seven centimetres now .
03:36	Just watch out . It's 9 11 centimeters . That
03:38	goes all the way here we are looking for this
03:41	To hear . Okay , now the width . What
03:44	have we got ? It's this particular shape here ,
03:46	it's times two cm and all right , So what
03:50	do we have ? Seven times two we have 14
03:53	centimeters squared . So this is just a little hint
03:55	here . I recommend if you get stuck on these
03:57	and you frequently get these wrong as you go along
03:59	and get the sidelines wrong . Go through and trace
04:03	them with your pen like this as you do them
04:05	. And it will probably guide your eye and make
04:07	it a lot easier for you . So what is
04:10	the total area here ? Well , it's going to
04:13	be equal to area one plus area to We're gonna
04:16	add these two guys together . So area one which
04:19	is 20 for an area to which is 14 .
04:22	We're gonna go 24 plus 14 and this is in
04:26	centimeters squared . This would be equal to 38 cm
04:32	two . Pretty simple . Right , okay , that's
04:35	the first one . So go through and do those
04:37	steps and those little tips off said and you're gonna
04:40	go okay , what about we have a look at
04:42	this on another example . Okay , for example ,
04:44	number two , once again we have very rectangular shapes
04:47	here , very blocky sort of shape looks like a
04:49	bit of a you and we're going to work out
04:52	the area within it . So first off put the
04:54	measurements into the required or the same base units ,
04:56	they're all in centimeters and I'm happy with centimeters that
04:59	hasn't asked for anything in particular . So the answer
05:01	is end up going to be in centimeters squared .
05:04	So let's break it now into simpler shapes . Now
05:08	we can go through and break this into three rectangles
05:10	. There would be a totally valid thing to do
05:12	is to break this up into three rectangles , 12
05:14	and three . Work out the area of each and
05:17	then add these together to get the total area .
05:20	But I'm gonna do this slightly differently . There's a
05:22	different way you can do this which gives you the
05:23	same answer . I'm going to start off with a
05:27	big rectangle here . This is going to be my
05:29	big rectangle , This entire part right here , I'm
05:33	going to call that rectangle one And from that I'm
05:37	going to take away rectangle two , that's this guy
05:41	in here . So we're gonna get rectangle one and
05:43	we're going to take away rectangle too . Also a
05:47	valid way of doing this . So let's do that
05:49	. We have rectangle one which is this entire shape
05:51	here . So let's get this first . The area
05:54	of rectangle one is equal to the length times the
05:58	width . Okay , so what's the length here ?
06:00	Well we know that we have this one here which
06:03	is seven centimetres . So we have this side but
06:07	we need This side . What's that going to be
06:09	? It's going to be three plus three plus two
06:13	. You can see it's this side plus this side
06:15	plus this side . Three plus three plus two equals
06:18	eight . So seven times eight centimeters . This is
06:22	equal to 56 centimeters squared . This is area one
06:28	. Okay , let's work out now . Rectangle number
06:30	two . The little one here . Okay , we
06:32	have this area which is equal to the length times
06:36	the width . All right , let's do this .
06:38	We have a length which is four centimeters And we
06:41	have a width . Which is this one here ,
06:44	which is three cm 4 times three . We have
06:47	an area of 12 cm squared . So how are
06:52	we working this out ? Well , our total area
06:54	is going to equal our rectangle one minus rectangle too
07:00	. So what does this Eagle rectangle one is 56
07:04	we're taking away 12 . What do we get ?
07:07	56 ? Take away 12 . We get our answer
07:10	of 44 cm squared . All right . So hopefully
07:15	you got that and that was really good . Maybe
07:17	you broke that up to three different rectangles and maybe
07:19	you want to do that right now ? Just to
07:20	check . But if you do that , you'll also
07:22	get that same answer Of 44 cm two . Not
07:26	too bad . Follow the steps , you'll be fine
07:29	. Now we're gonna get to some more tricky ones
07:31	. So let's do that . Okay . To our
07:33	third example , we have this rectangle here , which
07:37	has a triangle , take it out of it .
07:39	So , we're going to work out the area within
07:41	this shape here . So , first thing put the
07:44	measurements into the same base units . Into the required
07:46	base units . This one we're looking for the same
07:48	base units because we have meters meters meters meters ,
07:52	but this one is in millimeters . Yeah , I
07:55	have other videos . We'll look at how to convert
07:57	between measurements here and this is what you'll have to
07:59	do here . We have millimeters to meters . There
08:03	is 1000 millimeters which is equal to one m .
08:07	So we go 11,000 divided by 1000 . This is
08:11	equal to 11 m . So do that step first
08:14	, the second step break into simpler shapes . So
08:17	what shapes do we have here ? As I said
08:19	at the start , we have this big rectangle here
08:23	. So we have the first shape , shape number
08:25	one , which is the rectangle . Then what we
08:28	have is this second shape here , which is a
08:31	triangle . Okay , so shape number one . And
08:34	shape number two . Let's work out areas here .
08:37	So first off , let's work at the area of
08:40	a rectangle . We have a rectangle where the area
08:43	is equal to the length times width . And what's
08:46	the length of this one From here to here is
08:49	11 m and this is multiplied by six m ,
08:55	So 11 times six is 66 m squared . Okay
09:01	, that's the area of a rectangle there . Our
09:04	second shape that we have is the triangle . And
09:07	the area of a triangle , as you may remember
09:10	is half the base times the height . Let's work
09:13	out how area of a triangle here . So what
09:16	do we have ? We have the base here .
09:18	Now from here to here , this is our base
09:21	. How big is this ? Now ? You're gonna
09:22	see we have 11 m going across here . This
09:25	is too . And this is one so 11 take
09:28	away to take away one . This is eight m
09:32	. So , it's going to be half times eight
09:35	Times this height here , and now . We have
09:37	the height which is five m . So multiplied by
09:40	five m . All right . So , what's the
09:43	answer when we do this ? Half of eight ,
09:45	Which is four times five . This is 20 m
09:50	squared . All right . So how are we going
09:52	to work out our answer now ? We're going to
09:54	get the area of the rectangle and we're gonna subtract
09:57	the area of the triangle 66 . Take away 20
10:02	. If we do that , 66 take away 20
10:05	we get an answer which is 44 m squared .
10:09	Alright , cool . Hopefully got that answer as well
10:11	. And look , we're going along quite well here
10:14	. So , let's go to our final question that
10:16	we had . Okay , final question , what do
10:18	we have here ? As you can see , we
10:20	have a rectangular shape . I guess you could almost
10:22	put a little line down here and you might be
10:25	able to see it a little bit better . But
10:26	we have this rectangular shape . And to it we
10:29	have a semicircle of half circle attached to it .
10:32	So we're going to work out the area of our
10:34	rectangle and they were going to work out the area
10:36	of our half circle . We're gonna add these two
10:38	guys together . So let's do that . So first
10:41	off , put the measurements into the required or the
10:43	same base units . Now look , I'd be putting
10:45	this in two m . I think it makes more
10:47	sense . And as we said before , there's 1000
10:50	millimeters equals one m . So let's change this here
10:55	across two m . This is equal to six m
10:59	. Cool . All right , so let's go through
11:02	and now work out our shape . So , first
11:05	off , we have the simpler shapes which are broken
11:06	up here . We have shape number one here ,
11:08	which is a rectangle . And we have shape number
11:11	two here , which is a semi circle . So
11:14	let's work out our areas . Okay , shape number
11:16	one here , we have a rectangle where the area
11:19	is equal to the length times the width . All
11:23	right , let's do this . Okay , so what
11:25	is the length of this shape here ? It's six
11:27	m . What's the width of this ? It's for
11:31	matters . So , 6424 . We have our area
11:35	of 24 m squared . All right . Now ,
11:40	we're going to work out the second area that we
11:42	have here , which is of a semicircle . And
11:45	how we're gonna work that out ? Well , we're
11:47	gonna work out the area of a circle which is
11:49	pi R squared , and we're going to have our
11:51	answer . So the area of a circle or the
11:54	error I guess of a semicircle is going to be
11:56	pi R squared Divided by two . We're going to
12:00	have our answer . All right . So pi is
12:02	equal to pi and the radius here , is this
12:06	halfway measurement , As you can see the halfway of
12:08	this entire circle . If I was to put the
12:10	whole lot out Would be from the center to the
12:13	edge , would be three m . So three times
12:17	three because we have square , which is the radius
12:19	squared three times three . And this is over too
12:23	. If we work this out , well , what
12:25	do we get ? We get our answer which is
12:27	going to be 14 for leaders squared . All right
12:34	, cool . How do we go through and work
12:37	this out ? Well , we're going to get area
12:40	number one here and we're going to add area number
12:44	two to it . So the area of one plus
12:47	the area of two . We can do that fairly
12:50	simply without rewriting everything . 24 plus 14 point for
12:54	our answer is going to be 38 .4 m squared
13:01	. Anyway . That's how you go through and work
13:03	out the area of composite shapes . It's really not
13:05	a very hard thing to do . You just have
13:07	to be systematic about how you do it . Break
13:09	it up into those particular shapes . It doesn't matter
13:11	. You might have 4567 shapes . Break it up
13:15	into those shapes and slowly and systematically go through and
13:18	work out the areas of each and then add and
13:21	subtract using logic as you go along . Anyway .
13:25	Hopefully you like that video and hopefully it was some
13:27	help if you like the video and give me a
13:28	big thumbs up and put a comment in . The
13:30	comments . Thank you for watching . We'll see you
13:32	next time . Bye .

Summarizer

DESCRIPTION:

OVERVIEW:

Find the Area of Composite Shapes Easily - How to work out the Area of ANY Composite Figure. is a free educational video by tecmath.

This page not only allows students and teachers view Find the Area of Composite Shapes Easily - How to work out the Area of ANY Composite Figure. videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.