Area of composite (compound) shapes - Free Educational videos for Students in K-12 | Lumos Learning

Area of composite (compound) shapes - Free Educational videos for Students in k-12


Area of composite (compound) shapes - By tecmath



Transcript
00:01 Okay . This video is about problems to do with
00:03 the area . The first set , I'm gonna have
00:05 a look out here is to do with flooring .
00:08 So here's a house plant here . Say , what
00:11 you have to do is you have to put chipboard
00:13 all over the floor of this house . But the
00:16 chipboard Measures 3600 x 900 . Well , how many
00:23 pieces of chipboard you're going to need ? Let's work
00:26 out this problem . It's going to take a number
00:27 of steps . What we're gonna have to work out
00:30 , We're gonna have to work out area that the
00:33 whole floor covers , as well as the area of
00:36 the chipboard itself . We're gonna have to use these
00:38 figures to work and how many pieces of what we
00:40 need . They're going to approach this problem from a
00:43 different angle , we're going to actually lay the chipboard
00:45 down just to see if there's any difference and then
00:47 how we might cater for these differences . So first
00:52 off , we'll work out the area of the floor
00:54 itself . What we'll do is we split it up
00:58 and then we end up With two little sections ,
01:01 a little section that's all the area of that is
01:04 going to be equal to 5.09 x 4.2 . And
01:09 the answer to this is 21.38 m . Notice that
01:13 I have this tendency to actually change everything two m
01:16 . I generally find it was the most ordering occurs
01:18 in m squared . You may want to change all
01:20 your measurements to meet us first , the area of
01:24 the one beneath it , It's going to be 12
01:27 x 8.8 m . Which is going to give you
01:29 a total of 105 m squared . Total those ones
01:33 altogether 29.38 plus 105.6 . This is a total floor
01:38 space of 126.98 m or roughly 127 m , which
01:44 will put up the top . Now , the next
01:47 thing we're going to have to look at is the
01:49 area of the chip port itself . Okay . The
01:53 chipboard measures 3.6 m by 0.9 m , 3.6 x
02:01 .9 gives us an answer . A . which will
02:05 just under our little thing where I wrote , Well
02:08 how big the floor was . So the floor is
02:10 127 . Very the chipboard is 3.24 m . Okay
02:16 , final thing we have to find out is how
02:18 many pieces of the chip border needed . We will
02:21 work this out by getting the area the floor and
02:24 dividing into it area of each bit of checkpoints .
02:28 So 127 m squared , divided by 3.24 m squared
02:33 , Gives us 39.2 You can't buy 39.3 pieces of
02:38 chipboard . 40 pieces . Okay , so let's see
02:43 how this actually compares to if we go through and
02:46 we lay out each bit of chipboard , because this
02:50 has been done right now , As you can see
02:54 , hold up , We need 48 pieces of chipboard
02:58 . It's a bit of a difference from what we
03:00 actually worked out . We said we only needed 40
03:01 piece that we worked it out using area . We
03:04 lay it out and it looks like we actually need
03:06 48 piece as well . We can see the reason
03:10 for this . We go through on our plan here
03:12 and start actually removing the pieces of chipboard which could
03:15 be sourced as off cuts from elsewhere on the actual
03:19 plan . So we do that Well , we can
03:22 see is there's five pieces of chipboard here that actually
03:26 couldn't easily be gotten as off cards . It's at
03:30 48 take away . five Gives us about 43 pieces
03:33 that we do it this way . It's still a
03:35 little bit over . So , what I actually recommended
03:38 you call it around about a 10% wastage . If
03:40 you're working it out from the actual numbers , what
03:43 we did originally . Okay , so that would be
03:46 about 44 sheets . So that's how you work at
03:51 that sort of problem . There's a few things to
03:53 consider , but it's really , really worth knowing how
03:56 to do . Now let's consider a different problem involving
03:59 area . Here's a little problem here regarding a brick
04:03 wall . Now , put a brick wall , we
04:05 did the ancients given , but we don't need to
04:09 put bricks in where there's a window and there's a
04:10 door . So we're gonna have to work out all
04:12 up how much area we need on top of this
04:14 a little bit later , I'm gonna give you a
04:16 little bit where it's going to say there's miss many
04:18 bricks per square meter . How many bricks do we
04:19 need ? So the first thing we have to work
04:22 out will actually be what the actual area of the
04:25 brick part of the wall is . Okay . First
04:28 of all , if we look at the actual entire
04:30 wall , including the windows and doors , okay ,
04:35 They're at this wall here , it's going to be
04:37 13.7 by 2.4 Which equals 32.8 m squared . Okay
04:44 ? So what's working in the area of the window
04:46 that we have to get rid of ? Year of
04:48 the window Is 1.8 x 1.8 Which is going to
04:52 be 3.24 m squared . We're gonna end up getting
04:56 rid of that . Okay , the next we're going
04:58 to work out the air of the door , another
04:59 area which we're going to have to get rid of
05:01 . Okay , This is going to be 2.1 x
05:06 0.9 m . The answer to this , which is
05:08 1.89 m squared . So this is another area we're
05:12 going to have to get rid of . So all
05:15 of the area in total is gonna be the area
05:17 of the wall . Take by the area of the
05:18 window in the area of the door , which is
05:20 32.88 take away 3.24 take away , Which leaves us
05:25 with 27.75 m square . So the area of the
05:30 brick part of the wall is just under 28 m
05:33 squared . We'll take this problem just one little step
05:37 further . Say that you get 49 bricks per square
05:42 meter . Well , how many bricks are you going
05:44 to need for the entire job ? So what we
05:47 have to do is get 49 times by the 27.75
05:51 , Which gives us 1363 . Yeah . Well ,
05:56 at a 10% wastage to this . So 10%, ,
06:00 1360 , So 30 and 60 plus 136 means it
06:06 all up . We'd need 1496 breaths for this lovely
06:11 role here . Okay . These are just talk to
06:15 the top examples you get with using area . Okay
06:19 , So good practice . Good luck on this by
Summarizer

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