1
00:00:00,427 --> 00:00:06,537
This video is aneat Pereemeter n Aurie,

2
00:00:07,867 --> 00:00:11,183
Ah'l dae Pereemeter oan the cair
n Aurie oan the richt.

3
00:00:11,183 --> 00:00:16,443
Ye'r proablie fameeliair wi the idea,
bit we'l revisit it in case ye'r no.

4
00:00:16,443 --> 00:00:20,533
Pereemeter is the distance
tae gae around somit,

5
00:00:20,533 --> 00:00:24,093
Gif ye were tae pit ae fence aroond
or measure somit.

6
00:00:24,093 --> 00:00:27,750
Gif ye wer tae pit ae tape roond ae figure
hou lang that tape wid be.

7
00:00:27,750 --> 00:00:35,447
Sae, gif Ah hae ae rectangle,
n ae rectangle is ae figure

8
00:00:35,447 --> 00:00:40,140
that haes fower n fower richt angles.

9
00:00:40,140 --> 00:00:46,537
This is ae rectangle here,
Ah hae, 1, 2, 3, 4 richt angles n 4 sides,

10
00:00:46,537 --> 00:00:53,537
n the opposite sides ar equal in langth.

11
00:00:53,537 --> 00:01:00,923
Mibbe Ah'l lable the points,
A, B, C, n D,

12
00:01:00,923 --> 00:01:02,873
n lat's say that we ken the folaein,

13
00:01:02,873 --> 00:01:06,947
we ken that AB = 7,

14
00:01:06,947 --> 00:01:12,673
n we ken that BC is equal tae 5.

15
00:01:12,673 --> 00:01:17,443
We want tae ken whit
the pereemeter o ABCD is.

16
00:01:17,443 --> 00:01:26,363
The pereemeter o rectangle ABCD
is equal tae

17
00:01:26,363 --> 00:01:28,070
the sum o the langth o the sides.

18
00:01:28,070 --> 00:01:30,228
Gif Ah wis tae big ae fence

19
00:01:32,438 --> 00:01:35,281
Ah'd hae tae mesure hou lang this side is,

20
00:01:35,281 --> 00:01:36,800
we awreadie ken that that's 7,

21
00:01:38,650 --> 00:01:45,612
That side ower thaur is 7 units lang,
7 plus, this langth wil be 5,

22
00:01:45,612 --> 00:01:51,200
Thay tell us that BC is 5,
DC is gaun tae be

23
00:01:51,200 --> 00:01:53,963
the same langth aes AB,
n that's 7 again.

24
00:01:55,663 --> 00:02:00,555
Sae DA or AD whitiver ye want tae caa it,
wid be the same langth aes BC,

25
00:02:00,555 --> 00:02:03,721
n that's 5 again,
sae plus 5 again.

26
00:02:03,721 --> 00:02:07,543
Sae ye hae 7 plus 5 is 12,
plus 7 plus 5 is 12 again,

27
00:02:07,543 --> 00:02:13,502
sae ye'r gaun tae hae ae pereemeter o 24.

28
00:02:14,012 --> 00:02:19,489
Ye coud gae the ither road,
lat's say that ye hae ae square

29
00:02:19,489 --> 00:02:25,250
This is ae byordinair case o ae rectangle,
ae square haes 4 sides

30
00:02:25,250 --> 00:02:29,112
n 4 richt angles n aw o the sides ar equal

31
00:02:29,112 --> 00:02:36,885
Sae lat me draw ae square here,
ma best attempt.

32
00:02:36,885 --> 00:02:46,473
Sae this is A, B, C, D, n we'r
gaun tae say that this is ae square,

33
00:02:46,473 --> 00:02:57,171
n lat's say that this square
haes ae pereemeter o 36.

34
00:02:57,171 --> 00:03:01,787
Sae, whits the langth o the 4 sides,
weel aw o the sides hae the same langth,

35
00:03:01,787 --> 00:03:09,587
Lat's caa thaim x, sae gif AB is x,
than BC is x, than DC is x, n AD is x.

36
00:03:09,587 --> 00:03:13,472
Aw o thir sides ar congruent,
thay aw hae the same langth,

37
00:03:13,472 --> 00:03:16,570
We caa that x, sae gif we want
tae fynd oot the pereemeter

38
00:03:16,570 --> 00:03:28,696
it'l be x + x + x + x, or 4x,
n that equals 36,

39
00:03:28,696 --> 00:03:32,812
thay gave us that in the proablem,
n tae solve this 4 * sommit is 36,

40
00:03:32,812 --> 00:03:34,905
ye coud solve that in ye'r heid,

41
00:03:34,905 --> 00:03:42,338
bit we coud deevide baith sides bi 4,
n ye get x = 9,

42
00:03:42,338 --> 00:03:47,047
sae this is ae 9 bi 9 square,
this width is 9,

43
00:03:47,047 --> 00:03:50,787
this is 9, n the heicht here
is 9 n aw.

44
00:03:50,787 --> 00:03:52,927
Sae that's pereemeter,

45
00:03:52,927 --> 00:03:58,284
Aurie is ae mesure o hou muckle space
dis this tak up in twa dimentions.

46
00:03:58,284 --> 00:04:05,084
N yin waa tae think oan aurie is
gif Ah hae 1 bi 1 square,

47
00:04:05,084 --> 00:04:07,993
N whan Ah say 1 bi 1
it means that ye yinlie hae tae speceefie

48
00:04:07,993 --> 00:04:11,702
2 dimentions fer ae square or rectangle,
cause the ither 2 ar gaun tae be the sam.

49
00:04:11,702 --> 00:04:14,851
Fer exaumple, ye coud caa this
ae 5 bi 7 rectangle,

50
00:04:14,851 --> 00:04:18,326
Cause richt awaa that says that
this side is 5 n that side is 5,

51
00:04:18,326 --> 00:04:20,523
this side is 7 n that side is 7,

52
00:04:20,523 --> 00:04:22,856
N fer ae square ye coud say
it's ae 1 bi 1 square

53
00:04:22,856 --> 00:04:26,310
Cause that speceefies aw o the sides,
ye coud realie say fer ae square

54
00:04:26,310 --> 00:04:34,243
where 1 side is 1 than aw sides ar 1,
sae this is ae 1 bi 1 square.

55
00:04:34,243 --> 00:04:37,038
Ye can see the aurie o onie figure aes

56
00:04:37,038 --> 00:04:41,502
hou monie 1 bi 1 squares
can ye fit oan that figure?

57
00:04:41,502 --> 00:04:45,594
Sae, fer exaumple, gif we were
gaun back tae this rectangle here,

58
00:04:45,594 --> 00:04:48,634
n Ah wantit tae fynd oot
the aurie o this rectangle,

59
00:04:48,634 --> 00:04:52,715
n the notation that we can uise fer aurie
is tae pit sommit in brackets,

60
00:04:52,715 --> 00:04:59,717
Sae the aurie o rectangle ABCD,
A, B, C, D,

61
00:04:59,717 --> 00:05:04,262
is equal tae the nummer o 1 bi 1 squares
that we can fit oan this rectangle

62
00:05:04,262 --> 00:05:07,440
Lats ettle tae dae that bi haund,
Ah think... [Bletherin],

63
00:05:09,420 --> 00:05:14,337
Lats pit nummer o 1 bi 1s, lat's see,
we hae 5 1 bi 1 Squares this waa,

64
00:05:14,337 --> 00:05:17,366
n 7 this waa, sae Ah'm gaun tae
dae ma best tae draw it tydie,

65
00:05:17,366 --> 00:05:26,444
Sae that's 1, 2, 3, 4, 5, 6,
n than 7,

66
00:05:26,444 --> 00:05:29,263
1, 2, 3, 4, 5, 6, 7,

67
00:05:29,263 --> 00:05:37,211
Sae gaun alang 1 o the sides lik this,
ye coud pit 7 alang 1 side.

68
00:05:37,211 --> 00:05:44,144
N than ower here hou monie can we,
lat's see, that's 1 raw, that's twa raws,

69
00:05:44,144 --> 00:05:50,802
N we hae three raws, n than 4 raws,
n than 5 raws, 1, 2, 3, 4, 5,

70
00:05:50,802 --> 00:05:54,592
N that maks sence,
caus this is 1, 1, 1, 1, 1,

71
00:05:54,603 --> 00:05:58,853
Shid eik up tae 5,
thir's 1, 1, 1, 1, 1, 1, 1,

72
00:05:58,863 --> 00:06:01,466
Shid eik up tae 7,
Ay, thaur's 7.

73
00:06:01,466 --> 00:06:05,153
Sae this is 5 bi 7,
n ye cou d coont thir,

74
00:06:05,153 --> 00:06:08,260
n this is strechtfowerd multipleecation,
gif ye wantit tae ken

75
00:06:08,260 --> 00:06:10,147
the hale nummer o cubes,
ye coud coont thaim,

76
00:06:10,147 --> 00:06:13,036
or ye coud say, Ah hae 5 raws,
7 coloumns,

77
00:06:13,036 --> 00:06:16,668
Ah'm gaun tae hae 35 -- did Ah say cubes?,
squares --

78
00:06:16,668 --> 00:06:19,590
Ah hae 5 squares in this direction,
n 7 in this direction,

79
00:06:19,590 --> 00:06:22,025
Sae Ah'm gaun tae hae 35 squares aw up,

80
00:06:22,025 --> 00:06:27,035
Sae the aurie o this figure is 35,

81
00:06:27,037 --> 00:06:30,746
N sae the general methid, ye coud say,
Ah'm gaun tae tak 1 dimention

82
00:06:30,746 --> 00:06:32,750
n multiplie it bi the ither dimention

83
00:06:32,750 --> 00:06:44,081
Sae gif Ah hae ae rectangle,
lat's say the raectangle is 1/2 bi 2,

84
00:06:44,081 --> 00:06:46,926
Thae ar it dimentions,
ye can juist multiplie,

85
00:06:46,926 --> 00:06:50,232
1/2 * 2, the aurie is gaun tae be 1.

86
00:06:50,232 --> 00:06:52,720
Ye micht say, 'Whit dis 1/2 mean?',

87
00:06:52,720 --> 00:06:59,261
In this dimention it means that
Ah can yinlie fit 1/2 o ae 1 bi 1 square,

88
00:06:59,261 --> 00:07:02,485
Sae gif Ah want tae dae ae hale
1 bi 1 square, it's ae wee bit distortit,

89
00:07:02,485 --> 00:07:03,483
it wid lui lik that.

90
00:07:03,483 --> 00:07:07,577
Sae Ah'm yinlie daein 1/2 o 1,
Ah'm daein anither 1/2 o 1 juist lik that,

91
00:07:07,577 --> 00:07:12,957
n sae whan ye eik this n this thegeather,
ye'r gaun tae get ae hale 1,

92
00:07:12,957 --> 00:07:15,584
Nou, aneat the aurie o ae square,


93
00:07:15,584 --> 00:07:19,793
weel ae square's juist ae byordinair case
whaur the width n the langth ar the sam.

94
00:07:19,793 --> 00:07:24,353
Sae gif Ah hae ae square,
lat me draw ae square here.

95
00:07:25,480 --> 00:07:31,580
Lat's caa that x, y, z, lat's mak it s.

96
00:07:31,580 --> 00:07:34,100
Lat's say that Ah wantit
tae fynd the aurie,

97
00:07:34,100 --> 00:07:37,583
n lat's say that yin side here is 2,
sae XS is equal tae twa,

98
00:07:37,583 --> 00:07:41,516
n Ah want tae fynd the aurie o [XYZS],


99
00:07:41,516 --> 00:07:45,632
sae yince mair Ah uised the brackets
tae speceefie the aurie o this figure

100
00:07:45,632 --> 00:07:48,834
o this poliegon here, this square,
n we ken that it's ae square.

101
00:07:48,834 --> 00:07:50,561
We ken that aw o the sides ar equal.

102
00:07:50,561 --> 00:07:52,934
Weel, it's ae byordinair case
o ae rectangle,

103
00:07:52,934 --> 00:07:56,345
we multiplie the langth bi the width,
we ken that thay'r the same thing,

104
00:07:56,345 --> 00:08:00,660
Gif this is 2, than this is 2,
sae ye juist multiplie 2 bi 2,

105
00:08:00,660 --> 00:08:02,788
Or, gif ye want tae think o it
ye square it,

106
00:08:02,788 --> 00:08:04,887
That's whaur the word comes fae,
squarein sommit.

107
00:08:04,887 --> 00:08:09,787
Sae ye multiplie 2*2,
that's equal tae 2 squared,

108
00:08:09,787 --> 00:08:12,835
That's where the word comes fae,
fyndin the aurie o ae square.

109
00:08:12,835 --> 00:08:16,105
That's equal tae 4.

110
00:08:16,105 --> 00:08:23,635
N ye can see that ye can easielie fit
4 1 bi 1 squares oan this 2 bi 2 square.