This video is aneat Pereemeter n Aurie,
Ah'l dae Pereemeter oan the cair n Aurie oan the richt.
Ye'r proablie fameeliair wi the idea, bit we'l revisit it in case ye'r no.
Pereemeter is the distance tae gae around somit,
Gif ye were tae pit ae fence aroond or measure somit.
Gif ye wer tae pit ae tape roond ae figure hou lang that tape wid be.
Sae, gif Ah hae ae rectangle, n ae rectangle is ae figure
that haes fower n fower richt angles.
This is ae rectangle here, Ah hae, 1, 2, 3, 4 richt angles n 4 sides,
n the opposite sides ar equal in langth.
Mibbe Ah'l lable the points, A, B, C, n D,
n lat's say that we ken the folaein,
we ken that AB = 7,
n we ken that BC is equal tae 5.
We want tae ken whit the pereemeter o ABCD is.
The pereemeter o rectangle ABCD is equal tae
the sum o the langth o the sides.
Gif Ah wis tae big ae fence
Ah'd hae tae mesure hou lang this side is,
we awreadie ken that that's 7,
That side ower thaur is 7 units lang, 7 plus, this langth wil be 5,
Thay tell us that BC is 5, DC is gaun tae be
the same langth aes AB, n that's 7 again.
Sae DA or AD whitiver ye want tae caa it, wid be the same langth aes BC,
n that's 5 again, sae plus 5 again.
Sae ye hae 7 plus 5 is 12, plus 7 plus 5 is 12 again,
sae ye'r gaun tae hae ae pereemeter o 24.
Ye coud gae the ither road, lat's say that ye hae ae square
This is ae byordinair case o ae rectangle, ae square haes 4 sides
n 4 richt angles n aw o the sides ar equal
Sae lat me draw ae square here, ma best attempt.
Sae this is A, B, C, D, n we'r gaun tae say that this is ae square,
n lat's say that this square haes ae pereemeter o 36.
Sae, whits the langth o the 4 sides, weel aw o the sides hae the same langth,
Lat's caa thaim x, sae gif AB is x, than BC is x, than DC is x, n AD is x.
Aw o thir sides ar congruent, thay aw hae the same langth,
We caa that x, sae gif we want tae fynd oot the pereemeter
it'l be x + x + x + x, or 4x, n that equals 36,
thay gave us that in the proablem, n tae solve this 4 * sommit is 36,
ye coud solve that in ye'r heid,
bit we coud deevide baith sides bi 4, n ye get x = 9,
sae this is ae 9 bi 9 square, this width is 9,
this is 9, n the heicht here is 9 n aw.
Sae that's pereemeter,
Aurie is ae mesure o hou muckle space dis this tak up in twa dimentions.
N yin waa tae think oan aurie is gif Ah hae 1 bi 1 square,
N whan Ah say 1 bi 1 it means that ye yinlie hae tae speceefie
2 dimentions fer ae square or rectangle, cause the ither 2 ar gaun tae be the sam.
Fer exaumple, ye coud caa this ae 5 bi 7 rectangle,
Cause richt awaa that says that this side is 5 n that side is 5,
this side is 7 n that side is 7,
N fer ae square ye coud say it's ae 1 bi 1 square
Cause that speceefies aw o the sides, ye coud realie say fer ae square
where 1 side is 1 than aw sides ar 1, sae this is ae 1 bi 1 square.
Ye can see the aurie o onie figure aes
hou monie 1 bi 1 squares can ye fit oan that figure?
Sae, fer exaumple, gif we were gaun back tae this rectangle here,
n Ah wantit tae fynd oot the aurie o this rectangle,
n the notation that we can uise fer aurie is tae pit sommit in brackets,
Sae the aurie o rectangle ABCD, A, B, C, D,
is equal tae the nummer o 1 bi 1 squares that we can fit oan this rectangle
Lats ettle tae dae that bi haund, Ah think... [Bletherin],
Lats pit nummer o 1 bi 1s, lat's see, we hae 5 1 bi 1 Squares this waa,
n 7 this waa, sae Ah'm gaun tae dae ma best tae draw it tydie,
Sae that's 1, 2, 3, 4, 5, 6, n than 7,
1, 2, 3, 4, 5, 6, 7,
Sae gaun alang 1 o the sides lik this, ye coud pit 7 alang 1 side.
N than ower here hou monie can we, lat's see, that's 1 raw, that's twa raws,
N we hae three raws, n than 4 raws, n than 5 raws, 1, 2, 3, 4, 5,
N that maks sence, caus this is 1, 1, 1, 1, 1,
Shid eik up tae 5, thir's 1, 1, 1, 1, 1, 1, 1,
Shid eik up tae 7, Ay, thaur's 7.
Sae this is 5 bi 7, n ye cou d coont thir,
n this is strechtfowerd multipleecation, gif ye wantit tae ken
the hale nummer o cubes, ye coud coont thaim,
or ye coud say, Ah hae 5 raws, 7 coloumns,
Ah'm gaun tae hae 35 -- did Ah say cubes?, squares --
Ah hae 5 squares in this direction, n 7 in this direction,
Sae Ah'm gaun tae hae 35 squares aw up,
Sae the aurie o this figure is 35,
N sae the general methid, ye coud say, Ah'm gaun tae tak 1 dimention
n multiplie it bi the ither dimention
Sae gif Ah hae ae rectangle, lat's say the raectangle is 1/2 bi 2,
Thae ar it dimentions, ye can juist multiplie,
1/2 * 2, the aurie is gaun tae be 1.
Ye micht say, 'Whit dis 1/2 mean?',
In this dimention it means that Ah can yinlie fit 1/2 o ae 1 bi 1 square,
Sae gif Ah want tae dae ae hale 1 bi 1 square, it's ae wee bit distortit,
it wid lui lik that.
Sae Ah'm yinlie daein 1/2 o 1, Ah'm daein anither 1/2 o 1 juist lik that,
n sae whan ye eik this n this thegeather, ye'r gaun tae get ae hale 1,
Nou, aneat the aurie o ae square,
weel ae square's juist ae byordinair case whaur the width n the langth ar the sam.
Sae gif Ah hae ae square, lat me draw ae square here.
Lat's caa that x, y, z, lat's mak it s.
Lat's say that Ah wantit tae fynd the aurie,
n lat's say that yin side here is 2, sae XS is equal tae twa,
n Ah want tae fynd the aurie o [XYZS],
sae yince mair Ah uised the brackets tae speceefie the aurie o this figure
o this poliegon here, this square, n we ken that it's ae square.
We ken that aw o the sides ar equal.
Weel, it's ae byordinair case o ae rectangle,
we multiplie the langth bi the width, we ken that thay'r the same thing,
Gif this is 2, than this is 2, sae ye juist multiplie 2 bi 2,
Or, gif ye want tae think o it ye square it,
That's whaur the word comes fae, squarein sommit.
Sae ye multiplie 2*2, that's equal tae 2 squared,
That's where the word comes fae, fyndin the aurie o ae square.
That's equal tae 4.
N ye can see that ye can easielie fit 4 1 bi 1 squares oan this 2 bi 2 square.