A
"l
,l ,l J rl ,/ ,l d ,[ d d d ,/ J ,il t/ J *l *l J !t *l *l tl ''l -l '-l \.I 't {r \t \r
',
4
t
9.5
-
EXAMPLE
EXAMPLE
EFFECTS OF CHANGING DIMENSION$ ON AREA
2: Find the area of the isosceles triangle below, if its base
were doubled and height were tripled.
1: Find the area of the rectangle below.
Lo-=B cm
Proclu
o-{!:{{9
k= Lrbh= rzUDU.lS)
fY\wlhp
ly
e = lb,JE crnz
A("
What would happen if we changed one or both dimensions in this
rectangle?
Original
:Afea _
Ib'/3
Change in
Change in
width
L
Twice as
Twice as
lono
lono
4.2=2
q,lT.z_lsJg
rb{t
EXAMPLE
New I New Area
Area @
r
Z.tG=
_g$-.1
t rt f7 ^ t- II tt"
lLrl-a
6{.I5crnt
3:
I
as long j
--
tu
One-fourth
as long
Half
as long
lq,l7 - * =zfr
Prodr,cc-4
8y'3
=
"-"
3b,t-e(6) = Llb'ls
ol the 4ac.,brs
J-2.2=
Oriqr\al
J
'/-3
- A--
|
r
(No chongo!)
o-reo-"
tz,Xdr)
=+(tD)(8)3t{o
lb.7{g =
Jz,l3 e*
t.96
prodll:e* by or9r)'ral-oten
Find the area of the rhombus below if one diagonal was
halved and the other diagonal were doubled.
.3--lz
times
=3u{3
= 2,lbr[5 fnz
as long
Four
lb,l5
changed" triangle)
Three times
\bl[
{c-otors:
0ri3,\o-l spr@a-
= ^t'13(q)
Z
-lr
= lbv3 crn
'?oo
+1^4,
2.3= b
A=0w
c='{
c* o4
t
l€-^
tv.6- 2
A("changed" rhombut)
EXAMPLE
cLrc cJ"ar.3\ *hr- d rYncnSio rr5 , \ ou
3e+ *he nc\^r Wrea.
LIO,L
r"t1
4: The area of a triangle is 36 square tntllimeters.
Suppose the height was three times as long, and the
base was f our times as long. Find the area of the new
triangle.
What conjecture can you make regarding the changing of dimension(s) in a
two d imensional figure?
When yor hwlfrptV +ha orrgl'y\o.J o-rta
b1 *,1ne produ t+ o+ rhe 4.dcrors yo*
=
Prod*c+
o
f
+he 4actors
:
3'4 = !z
I
e = 137 rurn'
lYlulltp(V produc+ by ori3rho.,l oreq"
3b. tZ = lVz
1l
I
t
l
L
EFF ECTS OF GHANGING DIMENSIONS ON VOLUME
rlltiiiiijl
EXAMPLE 1: Find the Volume of the prism below.
Bh
V= lo(4)
-u=
a{@ oI fu+
4ft=h B=
V=
(
B=
{o
.l- =5
ft
EXAMPLE 2: Suppose the volume of a right triangular prism is
ftrrduc"|
5(2)
: lo 1+2
to Pf3
Original
Change
Change
Change
New
New Vol.
Volume
in leyoth
in width
in hgleht
Volume
Orig. Vol.
Twice as
Twice as
long
long
Three
times as
i{o
J.2= lo
long
No
Twice as
times as
Change
long
long
Half as
long
long
f,.{-- 10
{ ?of+'
ts'2-8'-
24ok3
2'*= i;I
Three
times as
long
4-3= 12
!
20.1.t2--
EXAMPLE
21c
21o
6
240 k3
1"
=lo
illl
what conjecture can you make regarding the effect of changing dimensions
on Volume?
{hee o r'igital v'lrrrn
vOlrrrne
fn\,\l+iP\\ *h
hcn Yor rn\,\ldPt\
b1 {hc produoF o{ -he $ac,tocs \ou
s.re ehangin3 the dtrncn6iorul , yDw
N
*hc
tl
ncw volwrne.
li
:
volt,.rne,:
\O8lC wnits3
6=lz
fr=
+'re {acrt'orr
2'3'* = 3
New vo\urne:
{8o
2.t'-2 4- 2-- 8
4 times as
Li
t2:
4.3=12
Three
S-3-- t<
t{o
2'2=4
lo.el.
J
f$wtlip\r1 Pro/uc* by origrna-l
3bO. j= lo8o
What would happen if we changed one or both dimensions in this
LIO
'
re c*o.rr3\c)
0w
=
36O cubic units. What would its new volume be if one of
its dimensions was twtce as long, a second dimension
was 1@times as long, and the third dimension was
AII as long?
3: Suppose the volume of a cube is 5+tl5 cubtc
centimeters. What would its new volume be if one of its
dimensions was halved, a second dimension was
doubled, and a third dimension did not change?
i'z't
=
I
No chan3e\
5\
,13 c,rn 3