Post on 08-Apr-2018
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 1/45
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 2/45
Group 1 Bernadeta Yosefani (02)
Gita Kartika Dewi (03)
Margaretha Revina (05)
Noer Aini Yulinar S. (07)
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 3/45
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 4/45
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 5/45
WHAT·S THE MEANING OF
PRISM??
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 6/45
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.
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 7/45
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.
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 8/45
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).
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 9/45
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).
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 10/45
The Name of Prism
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 11/45
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.
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 12/45
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
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 13/45
W HAT is Rectangular Prism ???
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 14/45
RECTANGULAR PRISM
� Is a prism that the
base have fourside
� Ex : square,
rectangle,rhombus, kite,
trapezoid, etc
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 15/45
edges top
base
high
vertex
The number of sides = 6
The number of edges = 12
The number of vertex = 8
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 16/45
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
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 17/45
K L
MN
O P
QR
KMQO
NL P R LMRO
KNQ PKLQR
O PMN
Cuboids has 6 Planes Diagonals
That are :
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 18/45
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
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 19/45
l
w
h
Volume cuboid:length x wide x high
Volume cube:s x s x s = s3
s
s
s
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 20/45
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
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 21/45
DRA W ING
RECTANGULAR
P RISM
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 22/45
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
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 23/45
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 24/45
A B
D C
EF
GH
J I
KM
LN
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 25/45
A B
D C
EF
GH
J I
KM
LN
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 26/45
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 27/45
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
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 28/45
Volume ofPrism
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 29/45
Volume: la x tp
Note:la = area of base
tp = high ofprism
Prism base
Prism high
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 30/45
Simple Note
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 31/45
Cube
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 32/45
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
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 33/45
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
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 34/45
CUBOID
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 35/45
� 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
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 36/45
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)
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 37/45
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 38/45
1. Given a rectangular prismmeasures 3 cm x 24 cm x 8 cm.
The total length of the edgesis«
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 39/45
Answer :
Formula:4l+4w+4h=4.3+4.24+4.8=12+96+32=140 cm
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 40/45
2. The surface area of a
rectangular prism with lengthof edges of 15 cm x 10 cm x 8cm is«
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 41/45
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
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 42/45
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«
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 43/45
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
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 44/45
Horeeii..!!!
8/6/2019 Math Prism
http://slidepdf.com/reader/full/math-prism 45/45