math prism

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Group 1 Bernadeta Yosefani (02)

Gita Kartika Dewi (03)

Margaretha Revina (05)

Noer Aini Yulinar S. (07)

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8/6/2019 Math Prism


WHAT·S THE MEANING OF

PRISM??

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P RISMIs a solid figure whichbounded by two

opposite faces whichare congruent anparallel and by other

faces which intersect atparallel edges.

Is a solid figure whichbounded by two

opposite faces whichare congruent anparallel and by other

faces which intersect atparallel edges.

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Prism base

Prism high

Opposite face

Opposite face

Parallel edges

Parallel edges

Is a solid figurewhich bounded by two opposite faces

which arecongruent anparallel and by otherfaces whichintersect at paralleledges.

Is a solid figurewhich bounded by two opposite faces

which arecongruent anparallel and by otherfaces whichintersect at paralleledges.

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CHARACTERISTIC OF

RECTANGULAR PRISM

Has a pair of parallel side that have same inshape and size that is called the base and thetop which have 4 sides

The vertex of top and bottom sides isconnected with the edges are parallel to each

other and the lengths are same. The edged iscalled as a vertical edge. The length of the edgeis the height of prism (h).

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edgestop

high

base

a pair of parallel side

1.Has a pair of parallel side thathave same inshape.

2.The vertex of top

and bottomsides isconnected with the edges.Thelength of theedge is the

height of prism(h).

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The Name of Prism

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The name of prism is determined

from the position of verticaledge and the base. If the baseshaped is n-sided regular, itmeans the prism is called prism n-

sided regular. If the vertical edge isperpendicular from the baseit·s called prism vertical n-

sided. If the vertical edgeisn·t perpendicular from thebase it·s called oblique prism.

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This is several kind of the special prism:

� Prism that all sides

shaped are square iscalled cube

� Prism that the base

shaped is square orrectangle is a cuboids

Cube

Cuboid

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W HAT is Rectangular Prism ???

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RECTANGULAR PRISM

� Is a prism that the

base have fourside

� Ex : square,

rectangle,rhombus, kite,

trapezoid, etc

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edges top

base

high

vertex

The number of sides = 6

The number of edges = 12

The number of vertex = 8

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Diagonal Planes

Diagonals plane is a plane that·s limited by twoedge of Cuboids that facing parallel and has

same length.

THE SHAPE OFDIAGONAL PLANES IN

THE FIGURE ISRECTANGLE

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K L

MN

O P

QR

KMQO

NL P R LMRO

KNQ PKLQR

O PMN

Cuboids has 6 Planes Diagonals

That are :

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V olume rectangular prism= V olume cuboid

V OLUME OF RECTANGULAR P RISM

= area of the cuboids base face x height of the cuboid

= area of prism base face x height of theprism

V = Lt

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l

w

h

Volume cuboid:length x wide x high

Volume cube:s x s x s = s3

s

s

s

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Example of V olume Question:

A rectangle prism have base withlength 5cm, wide 3cm, and the prismhigh is 8 cm.

Count the Volume!

Answer :

V olume= length x wide x high= 5 cm x 3 cm x 8 cm

= 120 cm³ 5 cm

8 cm

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DRA W ING

RECTANGULAR

P RISM

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1st :Draw two shape that

has 4 sides and the

size is same. It bethe base and top

2nd : Draw four connected

lines which

perpendicular. Then,

it be the height of

prism.

Top

Base

Height

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A B

D C

EF

GH

J I

KM

LN

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A B

D C

E F

GHSurface Area=2 x la+ ka x tp

Note:la = area of baseka = perimeter of base

tp = high of prism

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Volume ofPrism

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Volume: la x tp

Note:la = area of base

tp = high ofprism

Prism base

Prism high

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Simple Note

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Cube

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Element :

1. 6 faces that have same shape and size, are ABCD, EFGH, ABFE, DCGH, ADHE, and BCGF.

2. 12 edges with equal in length, are AB, BC, CD,DA,EF, FG, GH, HE, AE,BF, CG, and DH

3. 8 vertexes, are A,B,C,D,E,F,G,H

A B

D

C

E

F

GH

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6. 4 space diagonals, are GA, HB, FD, andEC.

5. 6 diagonal planes, are ABGH, CDEF, ADGF, BCHE, ACGE, and BDHF.

4. 12 face diagonals, are AF,BE,DG,CH,BG,CF,AH, DE,AC,BD, EG, and

FH

A B

D C

EF

GH

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CUBOID

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� Have 6 faces with 3 pairsof side that each pair have

rectangular shape andeach pair have size withthe same.there are ABCD and EFGH,

ABFE and DCGH, ADHEand BCGF.� Have 12 edges that

parallel edges have length

same.there are AB=CD=EF=GH,AD=BC=FG=EH,AE=DH=BF=CG A B

D

C

E F

GH

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Note:w = widthl = length

h = height

� Have 8 vertex

� Have 12 face diagonal� Have 6 diagonal planes

� Have 4 space diagonal

Volume = w x l x h

Surface area = 2 (w l + l h + w h)

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1. Given a rectangular prismmeasures 3 cm x 24 cm x 8 cm.

The total length of the edgesis«

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Answer :

Formula:4l+4w+4h=4.3+4.24+4.8=12+96+32=140 cm

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2. The surface area of a

rectangular prism with lengthof edges of 15 cm x 10 cm x 8cm is«

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Answer

Formula :2 x la + ka x tp =2 (15.10) + (15+10+15+10) x 8

= 2 (150) + 50 x 8= 300 + 400= 700 cm2

NOTE :

la=area of baseka=perimeter of base

tp=height of prism

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3. The length and the width of

rectangular prism are 9 cmand 8 cm respectively. Thetotal length of edges of therectangular prism equals tothe total length of edges of a

cube which has a volume of512 cm3 . The volume of therectangular prism is«

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3. S 3 = 512S =

3¥512

S = 8 cm

4(l+w+h) = 12 x s

4(9+8+h) = 12 x 89 + 8 + t = 12 x 8 : 417 + t = 24

t = 7

Total edges of rectangular prism= Total edges of cube

V olume = 9 x 8 x 7= 504 cm

3

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Horeeii..!!!

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math prism

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