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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Area of composite (compound) shapes is a free educational video by tecmath.
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