WEBVTT

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This video is aneat Pereemeter n Aurie,

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Ah'l dae Pereemeter oan the cair
n Aurie oan the richt.

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Ye'r proablie fameeliair wi the idea,
bit we'l revisit it in case ye'r no.

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Pereemeter is the distance
tae gae around somit,

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Gif ye were tae pit ae fence aroond
or measure somit.

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Gif ye wer tae pit ae tape roond ae figure
hou lang that tape wid be.

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Sae, gif Ah hae ae rectangle,
n ae rectangle is ae figure

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that haes fower n fower richt angles.

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This is ae rectangle here,
Ah hae, 1, 2, 3, 4 richt angles n 4 sides,

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n the opposite sides ar equal in langth.

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Mibbe Ah'l lable the points,
A, B, C, n D,

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n lat's say that we ken the folaein,

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we ken that AB = 7,

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n we ken that BC is equal tae 5.

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We want tae ken whit
the pereemeter o ABCD is.

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The pereemeter o rectangle ABCD
is equal tae

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the sum o the langth o the sides.

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Gif Ah wis tae big ae fence

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Ah'd hae tae mesure hou lang this side is,

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we awreadie ken that that's 7,

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That side ower thaur is 7 units lang,
7 plus, this langth wil be 5,

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Thay tell us that BC is 5,
DC is gaun tae be

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the same langth aes AB,
n that's 7 again.

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Sae DA or AD whitiver ye want tae caa it,
wid be the same langth aes BC,

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n that's 5 again,
sae plus 5 again.

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Sae ye hae 7 plus 5 is 12,
plus 7 plus 5 is 12 again,

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sae ye'r gaun tae hae ae pereemeter o 24.

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Ye coud gae the ither road,
lat's say that ye hae ae square

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This is ae byordinair case o ae rectangle,
ae square haes 4 sides

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n 4 richt angles n aw o the sides ar equal

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Sae lat me draw ae square here,
ma best attempt.

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Sae this is A, B, C, D, n we'r
gaun tae say that this is ae square,

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n lat's say that this square
haes ae pereemeter o 36.

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Sae, whits the langth o the 4 sides,
weel aw o the sides hae the same langth,

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Lat's caa thaim x, sae gif AB is x,
than BC is x, than DC is x, n AD is x.

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Aw o thir sides ar congruent,
thay aw hae the same langth,

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We caa that x, sae gif we want
tae fynd oot the pereemeter

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it'l be x + x + x + x, or 4x,
n that equals 36,

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thay gave us that in the proablem,
n tae solve this 4 * sommit is 36,

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ye coud solve that in ye'r heid,

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bit we coud deevide baith sides bi 4,
n ye get x = 9,

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sae this is ae 9 bi 9 square,
this width is 9,

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this is 9, n the heicht here
is 9 n aw.

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Sae that's pereemeter,

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Aurie is ae mesure o hou muckle space
dis this tak up in twa dimentions.

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N yin waa tae think oan aurie is
gif Ah hae 1 bi 1 square,

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N whan Ah say 1 bi 1
it means that ye yinlie hae tae speceefie

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2 dimentions fer ae square or rectangle,
cause the ither 2 ar gaun tae be the sam.

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Fer exaumple, ye coud caa this
ae 5 bi 7 rectangle,

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Cause richt awaa that says that
this side is 5 n that side is 5,

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this side is 7 n that side is 7,

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N fer ae square ye coud say
it's ae 1 bi 1 square

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Cause that speceefies aw o the sides,
ye coud realie say fer ae square

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where 1 side is 1 than aw sides ar 1,
sae this is ae 1 bi 1 square.

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Ye can see the aurie o onie figure aes

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hou monie 1 bi 1 squares
can ye fit oan that figure?

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Sae, fer exaumple, gif we were
gaun back tae this rectangle here,

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n Ah wantit tae fynd oot
the aurie o this rectangle,

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n the notation that we can uise fer aurie
is tae pit sommit in brackets,

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Sae the aurie o rectangle ABCD,
A, B, C, D,

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is equal tae the nummer o 1 bi 1 squares
that we can fit oan this rectangle

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Lats ettle tae dae that bi haund,
Ah think... [Bletherin],

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Lats pit nummer o 1 bi 1s, lat's see,
we hae 5 1 bi 1 Squares this waa,

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n 7 this waa, sae Ah'm gaun tae
dae ma best tae draw it tydie,

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Sae that's 1, 2, 3, 4, 5, 6,
n than 7,

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1, 2, 3, 4, 5, 6, 7,

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Sae gaun alang 1 o the sides lik this,
ye coud pit 7 alang 1 side.

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N than ower here hou monie can we,
lat's see, that's 1 raw, that's twa raws,

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N we hae three raws, n than 4 raws,
n than 5 raws, 1, 2, 3, 4, 5,

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N that maks sence,
caus this is 1, 1, 1, 1, 1,

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Shid eik up tae 5,
thir's 1, 1, 1, 1, 1, 1, 1,

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Shid eik up tae 7,
Ay, thaur's 7.

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Sae this is 5 bi 7,
n ye cou d coont thir,

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n this is strechtfowerd multipleecation,
gif ye wantit tae ken

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the hale nummer o cubes,
ye coud coont thaim,

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or ye coud say, Ah hae 5 raws,
7 coloumns,

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Ah'm gaun tae hae 35 -- did Ah say cubes?,
squares --

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Ah hae 5 squares in this direction,
n 7 in this direction,

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Sae Ah'm gaun tae hae 35 squares aw up,

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Sae the aurie o this figure is 35,

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N sae the general methid, ye coud say,
Ah'm gaun tae tak 1 dimention

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n multiplie it bi the ither dimention

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Sae gif Ah hae ae rectangle,
lat's say the raectangle is 1/2 bi 2,

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Thae ar it dimentions,
ye can juist multiplie,

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1/2 * 2, the aurie is gaun tae be 1.

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Ye micht say, 'Whit dis 1/2 mean?',

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In this dimention it means that
Ah can yinlie fit 1/2 o ae 1 bi 1 square,

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Sae gif Ah want tae dae ae hale
1 bi 1 square, it's ae wee bit distortit,

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it wid lui lik that.

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Sae Ah'm yinlie daein 1/2 o 1,
Ah'm daein anither 1/2 o 1 juist lik that,

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n sae whan ye eik this n this thegeather,
ye'r gaun tae get ae hale 1,

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Nou, aneat the aurie o ae square,


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weel ae square's juist ae byordinair case
whaur the width n the langth ar the sam.

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Sae gif Ah hae ae square,
lat me draw ae square here.

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Lat's caa that x, y, z, lat's mak it s.

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Lat's say that Ah wantit
tae fynd the aurie,

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n lat's say that yin side here is 2,
sae XS is equal tae twa,

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n Ah want tae fynd the aurie o [XYZS],


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sae yince mair Ah uised the brackets
tae speceefie the aurie o this figure

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o this poliegon here, this square,
n we ken that it's ae square.

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We ken that aw o the sides ar equal.

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Weel, it's ae byordinair case
o ae rectangle,

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we multiplie the langth bi the width,
we ken that thay'r the same thing,

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Gif this is 2, than this is 2,
sae ye juist multiplie 2 bi 2,

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Or, gif ye want tae think o it
ye square it,

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That's whaur the word comes fae,
squarein sommit.

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Sae ye multiplie 2*2,
that's equal tae 2 squared,

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That's where the word comes fae,
fyndin the aurie o ae square.

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That's equal tae 4.

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N ye can see that ye can easielie fit
4 1 bi 1 squares oan this 2 bi 2 square.