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
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