Important Concepts
Examples
The Measurement Process
•Identifyanobjectandtheattributeyouwanttomeasure.
•Selectanappropriateunit.
•Repeatedly“match”theunittotheattributeoftheobject.
•Determinethenumberofunits.
Tofindperimeter,countthenumberoflinearunits
neededtosurroundanobject.
Area and Perimeter of Rectangles
Tofindthearea,findthenumberofsquaresinonerow
(length)andmultiplybythenumberofrows (width).So,the
areaformulaisA = / * w.
Thereare5squaresinthe
firstrowand7rowsinall.
Theareaoftherectangle
is5 * 7 = 35squareunits.
Tofindtheperimeter,addthelengthandwidthanddouble
thatsum.Or,calculatetwolengthsplustwowidths.So,the
perimeterformulaisP = 2(/ + w)orP = 2/ + 2w.
Theperimeterofthe
rectangleis2(7 + 5)or
2 * 7 + 2 * 5 = 24 units.
Tofindarea,countthenumberofsquareunits
neededtocoveranobject.
Area and Perimeter of Triangles
Whenyousurroundatrianglewitharectangle,youcansee
thattheareaofthetriangleishalftheareaoftherectangle.
Youmayturnthetriangletoaconvenientsideasthebase,if
needed.So,theareaformulais 1
2 b * h,wherebisthebaseof
thetriangle(lengthoftherectangle)andhistheheightofthe
triangle(widthoftherectangle).
Tofindtheperimeter,measurethelengthsofthethreesides
andaddthemtogether.
Area and Perimeter of Parallelograms
Whenyoudrawadiagonalofaparallelogram,youform
two congruenttriangles.Theparallelogramandtrianglehave
thesamebaseandheight.So,theareaformulais2 * 1
2b * h orb * h.
(
)
Tofindtheperimeter,measurethelengthsofthefoursides
andaddthemtogether.
Volume of Right Rectangular Prisms
Countthenumberofunitcubesneededtofillanobject.Find
thenumberofcubesinthebaselayerandmultiplybythe
height.So,thevolumeformulaisV = Bh,whereBisthearea
ofbaseandhistheheight.Or,youcanmultiplythethree
dimensions.So,anotherformulaisV = / * w * h.
Surface Area of Prisms
Netsor“flatpatterns”aretwo-dimensionalrepresentationsof
three-dimensionalobjects.Tofindthesurfaceareaofaprism,
findthesumoftheareasofeachfaceofanetforthatprism.
ℓ
w
1
4
2
3
Triangle1iscongruentto
Triangle2.Triangle3is
congruenttoTriangle4.
7 ft
Theperimeterofthetriangle
is7 + 10 + 12.2,or29.2ft.
Theareaofthe
parallelogram
is6 * 4,or24cm2 .
10 ft
5 cm
Theperimeterofthe
parallelogramis2(5 + 6)or
2 * 5 + 2 * 6 = 22cm.
12.2 ft
4 cm
6 cm
Thevolumeofthe
rectangularprismis4(2)or
4 * 1 * 2 = 8 cm3 .
2 cm
1 cm
4 cm
5m
2m
S.A. = (2 * 3) + (5 * 2) + (5 * 3) +
(5 * 2) + (2 * 3) +
(5 * 3) = 62m2 .
5m
3m
2m
Finding Lengths in the Coordinate Plane
Ifthex-coordinates(ory-coordinates)arethesamefortwo
points,youcanfindthedistancebetweenthepointsby
findingtheabsolutevalueofthedifferenceoftheiry-values
(orx-values).
4
(−3, 2)
y
(4, 2)
2
x
4
2
O
2
2
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4
They-valuesare
equal,sothedistance
betweenthesepoints
is 0 - 3 - 4 0 ,or7units.