ó 10 ó 100 centimetres (cm) ì 10 ì 100 ì 1000

Transcription

1 REMEMBER 1. Te metri units of lengt re millimetres (mm), entimetres (m), metres (m) nd kilometres (km).. Use te tle elow to onvert metri units of lengt. ó 10 ó 100 ó 1000 millimetres (mm) entimetres (m) metres (m) kilometres (km) ì 10 ì 100 ì Wen onverting to lrger unit, divide. 4. Wen onverting to smller unit, multiply. 5. Te perimeter of spe is te totl distne round tt spe. 6. Te perimeter of retngle is given y te rule P = (l + w). 7. Te perimeter of squre is given y te rule P = 4l. EXERCISE 10A INDIVIDUAL PATHWAYS Ativity 10-A-1 Perimeters do-97 Ativity 10-A- More perimeters do-98 Ativity 10-A-3 Triky perimeters do-99 Perimeter FLUENCY 1 WE 1 Fill in te gps for e of te following. 0 mm = m 13 mm = m 130 mm = m d 1.5 m = mm e 0.03 m = mm f.8 km = m g m = m 400 mm = m = m i 1375 mm = m = m j.7 m = m = mm k 0.08 m = mm l km = m m 670 m = m n km = m WE Find te perimeter of te spes elow. 4 m 3 m 1 m 5 m 40 mm 31 mm 35 mm d 3 m m 1 m m 1.5 m 6 m e 60 mm f 11 mm 5 mm 44 Mts Quest 8 for te Austrlin Curriulum

2 g 9 mm 5.0 m 4.5 m.0 m i 14 mm j 9 mm 1.5 m 4 m 530 m 330 m k 0.6 m l.4 m 36 m 346 m UNDERSTANDING Welink Lengt onversions 3 Cipord seets re sold in tree sizes. Convert e of te mesurements elow into entimetres nd ten into metres: 1800 mm ì 900 mm 400 mm ì 900 mm 700 mm ì 100 mm. 4 A prtiulr type of in is sold for $.5 per metre. Wt is te ost of.4 m of tis in? 5 Fri is sold for $7.95 per metre. How mu will 4.8 m of tis fri ost? 6 Te stndrd mrton distne is 4. km. If mrton re strts nd finises wit one lp of Stdium Austrli, seen t rigt, wi is 400 m in lengt, wt distne is run on te rod outside te stdium? 7 Mri needs 3 piees of timer of lengts 100 mm, 65 m nd 450 mm to onstrut lotes rk. Wt is te totl lengt of timer required, in metres? How mu will te timer ost t $3.80 per metre? 8 WE 3 Find te perimeter of sketll ourt, wi is 8 m long nd 15 m wide. 9 A woven retngulr rug is 175 m wide nd 315 m long. Find te perimeter of te rug. 10 A line is drwn to form order m from e edge of piee of A4 pper. If te pper is 30 m long nd 1 m wide, wt is te lengt of te order line? 11 A retngulr pddok 144 m long nd 111 m wide requires new tree-strnd wire fene. Wt lengt of fening wire is required to omplete te fene? How mu will it ost to rewire te fene if te wire ost $1.47 per metre. Cpter 10 Mesurement 45

3 1 A omputer desk needs to ve tle edging. If te edging ost $1.89 per metre, find te ost of te tle edging required for te desk..1 m 150 mm 134 m.1 m 13 Clulte te unknown side lengts in e of te given spes. x m 4.9 m x m 5.8 m 8 m Perimeter = 30 m Perimeter = 176 m Perimeter = 3.4 m 14 WE 4 Te retngulr illord s perimeter of 5 m. Clulte its widt if te lengt is 7 m. 15 Te tiket t rigt s perimeter of 4 m. Clulte te unknown side lengt. Olivi wises to deorte te tiket y pling gold line long te slnted sides. How long is te line on e tiket? A ottle of gold ink will supply enoug ink to drw 0 m of line. How mny ottles of ink sould e pursed if 00 tikets re to e deorted? 11 m REASONING 16 A squre nd n equilterl tringle ve te sme perimeter. Te side of te tringle is 3 m longer tn te side of te squre. How long is te side of te squre? REFLECTION Wt is te est wy to rememer te units onversion rt? 10B Cirumferene Te irumferene (C) is noter term for te perimeter of irle. Te dimeter (D) of irle is te nme given to te strigt-line distne ross irle toug its entre. Te strigt-line distne from te entre of te irle to te irumferenes is lled te rdius. Tere is reltionsip etween te dimeter nd Dimeter te irumferene of irle. Te rtio C is pproximtely 3. Wen tis rtio is lulted extly, D Cirumferene Rdius it is lled pi or p. Te symol p represents te rtio of te irumferene of irle to its dimeter. It is n infinite, non-reurring nd non-terminting deiml tt egins s For prolem-solving purposes, 3.14 is good pproximtion for p. For etter ury, use speil utton on your lultor, lelled p. Te irumferene of irle is given y te formul C = p D. 46 Mts Quest 8 for te Austrlin Curriulum

4 A dimeter of irle is twie s long s its rdius, tt is, D = r. Terefore, te oter wy to write te formul for te irumferene is C = p r, were r is te rdius of irle. WORKED EXAMPLE 5 Find te irumferene of e of te following irles, giving nswers i in terms of p ii orret to deiml ples. 4 m 5 m THINK WRITE i 1 Write te formul for te irumferene of irle. Note: Sine te dimeter of te irle is given, use te formul tt reltes te irumferene to te dimeter. Sustitute te vlue D = 4 into te formul. 3 Write te nswer nd inlude te orret units. ii 1 Write te formul for te irumferene of irle. Sustitute te vlues D = 4 nd p = 3.14 into te formul. 3 Evlute nd inlude te orret units. i 1 Write te formul for te irumferene of irle. Note: Sine te rdius of te irle is given, use te formul tt reltes te irumferene to te rdius. Sustitute te vlue r = 5 into te formul. 3 Write te nswer nd inlude te orret units. ii 1 Write te formul for te irumferene of irle. Sustitute te vlues r = 5 nd p = 3.14 into te formul. i C = p D = p ì 4 = 4p m ii C = p D = 3.14 ì 4 = m i C = p r = ì p ì 5 = 10p m ii C = p r = ì 3.14 ì 5 3 Evlute nd inlude te orret units. = m Cpter 10 Mesurement 47

5 WORKED EXAMPLE 6 Find te perimeter of te spe t rigt, orret to deiml ples. 1 m THINK 1 Identify te prts tt onstitute te perimeter of te given spe. WRITE P = 1 irumferene + strigt-line setion Write te formul for te irumferene of irle. Note: If te irle were omplete, te strigtline segment sown would e its dimeter. So te formul tt reltes te irumferene to te dimeter is used. 3 Sustitute te vlues D = 1 nd p = 3.14 into te formul. 4 To find te perimeter of te given spe, lve te vlue of te irumferene nd dd te lengt of te strigt setion. P = 1 p D + strigt-line setion = 1 ì 3.14 ì = Evlute nd inlude te orret units. = m REMEMBER 1. Te rdius (r), dimeter (D) nd irumferene (C) of irle re sown t rigt.. Te irumferene of irle, C, is given y te formul C = p D, or C = p r, were D is te dimeter nd r is te rdius of irle. 3. p represents te rtio of te irumferene of irle to its Cirumferene Dimeter Rdius dimeter, tt is, C D. 4. Te numeril pproximtion for p is EXERCISE 10B Cirumferene FLUENCY 1 WE 5 Find te irumferene of e of tese irles, giving nswers i in terms of p ii orret to deiml ples. m 10 m 7 mm 48 Mts Quest 8 for te Austrlin Curriulum

6 INDIVIDUAL PATHWAYS d e f 0.8 m 7.4 km 34 m Ativity 10-B-1 Cirumferene do-300 Ativity 10-B- More irumferene do-301 Ativity 10-B-3 Advned irumferene do-30 WE 5 Find te irumferene of e of te following irles, giving nswers i in terms of p ii orret to deiml ples. 4 m 17 mm 8 m Intertivity Finding pi int-0079 d e f 1.43 km 0.4 m 10.6 m Digitl do Investigtion Te dimeter of irle nd its irumferene ny onnetion? do Coose te pproprite formul nd find te irumferene of tese irles. 77 km 6 m 48 mm d e f 1.07 m 31 mm 400 m 4 WE 6 Find te perimeter of e of te spes elow. (Rememer to dd te lengts of te strigt setions.) 4 m 16 mm 10 m (ontinued) Cpter 10 Mesurement 49

7 d e f 11 mm 18 m 0 m g i 75 m 48 m 30 m 1.4 m 50 m 1. m 5 MC Te irumferene of irle wit rdius of 1 m is: A p ì 1 m B ì p ì 1 m C ì p ì 4 m D p ì 6 m E p ì 18 m 6 MC Te irumferene of irle wit dimeter of 55 m is: A ì p ì 55 m B p ì 55 m C p ì 55 m D p ì 110 ì m E ì p ì 110 m UNDERSTANDING 7 In Pysis experiment, students spin metl weigt round on te end of nylon tred. How fr does te metl weigt trvel if it ompletes 10 revolutions on te end of 0.88 m tred? 8 A sooter tyre s dimeter of 3 m. Wt is te irumferene of te tyre? Nylon tred r = 0.88 m Weigt 9 Find te irumferene of te seweed round te outside of tis susi roll. 10 Find te irumferene of te Ferris weel sown elow. 19 mm 8 m 50 Mts Quest 8 for te Austrlin Curriulum

8 11 Clulte te dimeter of irle (orret to deiml ples were pproprite) wit irumferene of: m m 74.6 mm. 1 Clulte te rdius of irle (orret to deiml ples were pproprite) wit irumferene of: 1.6 m m 157 mm. 13 Clulte te rdius of tyre wit irumferene of m. 14 Clulte te totl lengt of metl pipe needed to ssemle te wding pool frme sown t rigt. r = 1.4 m 15 Ntn runs round te inside lne of irulr trk tt s rdius of 9 m. Rel runs in te outer lne, wi is.5 m furter from te entre of te trk. How mu longer is te distne Rel runs e lp? 40 m REASONING 16 In Around te world in eigty dys y Jules Verne, Piles Fogg osts tt e n trvel round te world in 80 dys or fewer. Tis ws in te 1800s, so e ouldn t tke plne. Wt verge speed is needed to go round te Ert t te equtor in 80 dys? Assume you trvel for 1 ours e dy nd tt te rdius of te Ert is pproximtely 6390 km. REFLECTION 17 Liesel s iyle overs 19 m in 10 revolutions of er iyle weel wile Jred s iyle overs 0 m in 8 revolutions of is iyle weel. Wt is te differene etween te rdii of te two iyle weels? If you needed to estimte te vlue of p using ny round ojet, ow would you do it? 10C Are of retngles, tringles, prllelogrms, romuses nd kites Are Te re of spe is te mount of flt surfe enlosed y te spe. Are is mesured in squre units, su s squre millimetres (mm ), squre entimetres (m ), squre metres (m ) nd squre kilometres (km ) Are units n e onverted using te rt elow. ó 10 ó 100 ó 1000 squre millimetres (mm ) 10 = 1 00 squre entimetres (m ) 100 = squre metres (m ) 1000 = squre kilometres (km ) ì 10 ì 100 ì 1000 Are units re te squres of tose for te orresponding liner units. Lrge res of lnd n e mesured in etres (). 1 = m. Cpter 10 Mesurement 51

9 WORKED EXAMPLE 7 Complete te following metri onversions km = m mm = m THINK Look t te metri onversion rt. To onvert squre kilometres to squre metres, multiply y ; tt is, move te deiml point 6 ples to te rigt. Look t te metri onversion rt. To onvert squre millimetres to squre metres, divide y ; tt is, move te deiml point 6 ples to te left. WRITE km = ì m = m mm = ó m = m WORKED EXAMPLE 8 Are of retngle Te re of retngle n e found using te formul A R = l ì w, were l is te lengt nd w is te widt of te retngle. Te re of squre n e found using te formul A S = l, were l is te side lengt of te squre. Find te re of retngle wit dimensions sown elow. 8 m 5.6 m THINK WRITE 1 Write te formul for te re of retngle. A = l ì w Identify te vlues of l nd w. l = 8 nd w = Sustitute te vlues of l nd w into te formul nd evlute. Inlude te pproprite units. A = 8 ì 5.6 = 44.8 m Are of tringle Te re of tringle, A T, is given y te formul A T = 1 ì ì, were is te se nd is te eigt of te tringle. Te se nd te eigt of tringle re perpendiulr (t rigt ngles) to e oter. 5 Mts Quest 8 for te Austrlin Curriulum

10 WORKED EXAMPLE 9 Find te re of e of tese tringles in te smller unit..8 m 55 m 7.5 m 1.8 m THINK WRITE 1 Write te formul for te re of tringle. A = 1 Identify te vlues of nd. = 7.5, =.8 3 Sustitute te vlues of nd into te formul. 4 Evlute. Rememer to inlude te orret units (m ). 1 Write te formul for te re of tringle. A = 1 A = 1 ì 7.5 ì.8 = 3.75 ì.8 = 10.5 m Convert mesurements to m. 1.8 m = 1.8 ì 100 m = 180 m 3 Identify te vlues of nd. = 180, = 55 4 Sustitute te vlues of nd into te formul. 5 Evlute. Rememer to inlude te orret units (m ). A = 1 ì 180 ì 55 = 90 ì 55 = 4950 m Digitl do Investigtion Are of prllelogrm do-319 Are of prllelogrm A prllelogrm is qudrilterl wit two pirs of prllel sides. E pir is of equl lengt. It n e divided into two tringles y drwing digonl. In te prllelogrm PQRS elow, re ΔPQR nd ΔRSP ongruent? As teir orresponding sides re of equl lengt, ten ΔPQR ô ΔRSP (SSS ongrueny ondition). P p q Q S s r R As te re of tringle is given s A T = 1 ì ì, ten te re of prllelogrm must e twie te re of e tringle, so A P, re of prllelogrm is given y te formul A P = ì, were is te se nd is te eigt of prllelogrm. Te se nd te eigt of prllelogrm re perpendiulr to e oter. Cpter 10 Mesurement 53

11 WORKED EXAMPLE 10 Find te re of te prllelogrm sown. THINK WRITE 1 Write te formul for te re of prllelogrm. A = Identify te vlues of nd. = 13, = 6 3 Sustitute 6 for nd 13 for. A = 13 ì 6 4 Multiply te numers togeter nd inlude te orret units. = 78 m 6 m 13 m Are of romus A romus is prllelogrm wit ll four sides of equl lengt nd e pir of opposite sides prllel. Te re of romus, A RH, is given s A RH = ì. Are of kite A kite is qudrilterl wit two pirs of equl, djent sides nd one pir of equl ngles. Te re of kite n e determined y dividing te kite into two equl tringles nd using te formul for te re of tringle. REMEMBER 1. Te re of spe is te mount of flt surfe enlosed y te spe.. Are is mesured in units sed on te squre metre, s sown in tis onversion rt. ó 10 ó 100 ó 1000 squre millimetres (mm ) 10 = 1 00 squre entimetres (m ) 100 = squre metres (m ) 1000 = squre kilometres (km ) ì 10 ì 100 ì 1000 Rell m = 1 etre = 1 Note: Te onversion is te squre of te equivlent liner onversion. 3. Te re of retngle is given y te formul A = l ì w, were l is te lengt nd w is te widt of retngle. 4. Te re of squre is given y te formul A = l. 5. Te re of tringle my e found using te rule A = 1, were is te se nd is te eigt of tringle. 6. Te se nd eigt of ny tringle re perpendiulr to e oter. 7. A prllelogrm is qudrilterl wit two pirs of prllel sides. 8. Te re of prllelogrm is given y te formul A =, were is te lengt of te se of te prllelogrm nd is its vertil eigt. 9. Te se nd te eigt of ny prllelogrm re perpendiulr to e oter. 54 Mts Quest 8 for te Austrlin Curriulum

12 EXERCISE 10C INDIVIDUAL PATHWAYS Ativity 10-C-1 Are of retngles, tringles nd prllelogrms do-303 Ativity 10-C- More re of retngles, tringles nd prllelogrms do-304 Ativity 10-C-3 Advned re of retngles, tringles nd prllelogrms do-305 Are of retngles, tringles, prllelogrms, romuses nd kites FLUENCY 1 WE 7 Complete te following metri onversions km = m 35 mm = m 540 m = mm d m = m e mm = m f m = km g m = 1.78 = m i m = mm j km = m WE 8 Find te re of e of te retngles elow. 9 m 4 m 45 mm 5 mm 3 m 1.5 m d 7 km 45 km e 5 m f 50 m 16 mm.1 m 3 Find te re of e of te squres elow. 5 mm 16 m Questions 4 nd 5 relte to te digrm t rigt. 4 MC Te eigt nd se respetively of te tringle re: A 3 mm nd 6 mm B 3 mm nd 134 mm C 3 mm nd 187 mm D 6 mm nd 187 mm E 134 mm nd 187 mm 5 MC Te re of te tringle is: A 99 mm B 99 mm C 5984 mm D 5984 mm E 618 mm 6 WE 9 Find te re of te following tringles in smller units. 6 mm.3 m 3 mm 187 mm 134 mm 37 mm 40.4 m 68 mm 87.7 m Cpter 10 Mesurement 55

13 31.8 mm d 85.7 mm 1.9 m m e 14.8 mm f.7 m 0.16 m 7 WE 10 Find te re of te prllelogrms sown elow. 11 mm 5 mm 10 m 00 m d 3 m.4 mm 0.5 m 4.6 mm e 1.8 m f 75 mm 3 mm 1.5 m g.8 m 7 m 6. m 68 m 70 m i 5.3 m 5.3 m 1.6 m 56 Mts Quest 8 for te Austrlin Curriulum

14 UNDERSTANDING 8 Zorko s divided is vegetle pt, wi is in te spe of regulr (ll sides equl) pentgon, into 3 setions s sown in te digrm t rigt. Clulte te re of e individul setion, orret to deiml ples. Clulte te re of te vegetle pt, orret to deiml ples. 5.3 m m m 8.89 m 9 Find te re of te tringle used to rk up te illird lls t rigt. 8.5 m 4.7 m 10 Te pyrmid t rigt s 4 identil tringulr fes wit te dimensions sown. Clulte: te re of one of te tringulr fes te totl re of te 4 fes. 11 Georgi is plnning to rete feture wll in er lounge room y pinting it different olour. Te wll is 4.6 m wide nd 3.4 m ig. 00 m Clulte te re of te wll to e pinted. Georgi knows tt 4 litre n of pint is suffiient to over 1 squre metres of wll. How mny ns must se purse if se needs to pply two ots of pint? 1 Clulte te se lengt of te give-wy sign t rigt. 13 Clulte te widt of retngulr sportsground if it s n re of 30 nd lengt of 750 m. Te wtering system t te sports ground overs 8000 squre metres in 10 minutes. How long does it tke to wter te sportsground? 45 m 150 m A = 945 m 14 Find te re of gold rid needed to mke te four militry stripes sown..1 m 6 m Cpter 10 Mesurement 57

15 15 Wt is te re of te lok of lnd in te figure t rigt? 76 m 7 m Welink Are of romus 16 MC Wi sttement out prllelogrm is flse? A Te opposite sides of prllelogrm re prllel. B Te eigt of te prllelogrm is perpendiulr to its se. C Te re of prllelogrm is equl to te re of te retngle wose lengt is te sme s te se nd wose widt is te sme s te eigt of te prllelogrm. D Te perimeter of te prllelogrm is given y te formul P = ( + ). E Te re of prllelogrm is given y te formul A =. 17 Te se of prllelogrm is 3 times s long s its eigt. Find te re of te prllelo grm, given tt its eigt is.4 m long. 18 A designer vse s squre se of side lengt 1 m nd four iden til sides, e of wi is prllelogrm. If te vertil eigt of te vse is 30 m, find te totl re of te glss used to mke tis vse. (Assume no wste nd do not forget to inlude te se.) 19 Find te lengt of te se of prllelogrm wose eigt is 5. m nd wose re is 18.7 m. Find te eigt of prllelogrm wose se is 7.5 m long nd wose re is 69 m. 0 Te lengt of te se of prllelogrm is equl to its eigt. If te re of te prllelo grm is 90.5 m, find its dimensions. REASONING 1 If te digonls of romus iset e oter nd interset t rigt ngles, use mtemtil resoning to sow nd explin tt A RH = 1 ì x ì y, were x nd y re te lengts of te digonls of te romus. Using mtemtil resoning, determine te re of te kite elow in terms of nd. REFLECTION Wy is it importnt to know tt te eigt nd te se of ny tringle nd ny prllelogrm re perpendiulr? 10D Digitl do Investigtion Are of irle do-31 Are of irle Te re of irle, A, n e found using te formul A = π r, were r is te rdius of te irle. r Te rdius of irle, r, is equl to lf of its dimeter, D: r = D. 58 Mts Quest 8 for te Austrlin Curriulum

16 WORKED EXAMPLE 11 Find te re of e of te following irles. 0 m 18 m THINK WRITE 1 Write te formul for te re of irle. A = p r Sustitute 0 for r nd 3.14 for p. A = 3.14 ì 0 3 Evlute (squre te rdius first) nd inlude te orret units. = 3.14 ì 400 = 156 m 1 Write te formul for te re of irle. A = p r We need rdius, ut re given te dimeter. Stte te reltion etween te rdius nd te dimeter. D = 18; r = D ó 3 Hlve te vlue of te dimeter to get te rdius. r = 18 ó = 9 4 Sustitute 9 for r nd 3.14 for p. A = 3.14 ì 9 = 3.14 ì 81 5 Evlute (squre te rdius first) nd inlude te orret units. = m REMEMBER 1. Te re of irle is given y te formul A = p r, were r is te rdius of irle nd p s n pproximte vlue of Te rdius of irle, r, is equl to lf of its dimeter, D: r = D. EXERCISE 10D INDIVIDUAL PATHWAYS Ativity 10-D-1 Are of irle do-306 Ativity 10-D- More irles do-307 Ativity 10-D-3 Advned lultions involving res of irles do-308 Are of irle FLUENCY 1 WE 11 Find te re of e of te following irles. 1 m.5 km Cpter 10 Mesurement 59

17 d 1.7 m 0.7 m e f 58 m 8.1 mm Find te re of: irle of rdius 5 m irle of rdius 1.4 mm irle of dimeter 8 m d irle of dimeter 18 m. UNDERSTANDING 3 Te word nnulus is te Ltin word for ring. An nnulus is te spe formed etween two irles wit ommon entre (lled onentri ir les). To find te re of n nnulus, lulte te re of te smller irle nd sutrt it from te re of te lrger irle. Find te re of te nnulus for te following sets of onentri irles. r r 1 r 1 = rdius of smller irle r = rdius of lrger irle Are nnulus = p r - p r 1 An nnulus is te sded re etween te onentri irles. 4 m m 41 m 7 m 50 m 81 m 60 Mts Quest 8 for te Austrlin Curriulum

18 4 Find te re of e of te following spes. 0 m 1 m d 16 mm 4. m e f 4 m 10 m g 6 m 7.5 m 5 m i.5 m 3 m 5 Find te minimum re of luminium foil tt ould e used to over te top of te irulr try wit dimeter 38 m. 6 Wt is te re of mteril in irulr mt of dimeter.4 m? 7 How mny pkets of lwn seed sould Jonne uy to sow irulr ed of dimeter 7 m, if e pket of seed overs 3 m? 8 A lndspe grdener wises to spred fertiliser on semiirulr grden ed tt s dimeter of 4.7 m. How mu fertiliser is required if te fertiliser is pplied t te rte of 0 g per squre metre? REFLECTION Tink of wy to rememer te differene etween te formul for te irumferene nd tt for te re of irle. Cpter 10 Mesurement 61

19 10E Are of trpeziums A trpezium is qudrilterl wit one pir of prllel sides. Te following figures re ll trpeziums. Digitl do Investigtion Are of trpezium do-30 Te eigt of te trpezium is perpendiulr to e of its prllel ses. To determine te re of trpezium, drw two lines to rete two tringles nd one retngle s sown. Pling te two tringles togeter retes one tringle nd one retngle. Te totl re of te two spes, A, will give A = ì + 1 ì ì ( - ). Simplifying tis gives A = 1 ( + ) ì. Te re of trpezium, A, is given y te formul A = 1 ( + ) ì, were nd re te lengts of prllel sides nd is te eigt of te trpezium. WORKED EXAMPLE 1 Find te re of te trpezium t rigt. 6 m 4 m 10 m THINK WRITE 1 Write te formul for te re of te trpezium. A = 1 ( + ) ì 6 Mts Quest 8 for te Austrlin Curriulum

20 Identify te vlues of, nd. Note: It does not mtter wi of te prllel sides is nd wi one is, sine we will need to dd tem togeter. = 10, = 6 nd = 4 3 Sustitute te vlues of, nd into te formul. A = 1 ì (10 + 6) ì 4 4 Evlute (work out te rkets first) nd inlude te orret units. A = 1 ì 16 ì 4 = 3 m REMEMBER Te re of trpezium is given y te formul A = 1 ( + ) ì, were nd re prllel sides nd is te eigt of trpezium. Te eigt of te trpezium is lwys perpendiulr to te prllel sides. EXERCISE 10E INDIVIDUAL PATHWAYS Ativity 10-E-1 Are of trpezium do-309 Ativity 10-E- More trpeziums do-310 Ativity 10-E-3 Advned trpeziums do-311 Are of trpeziums FLUENCY 1 WE 1 Find te re of e of te following trpeziums. 3 m m 6 m 9 m 4.5 m 6 m 5.0 m d 14 mm 18 mm 3.0 m 5 mm 3.5 m e 8.0 m f 0.9 m.4 m 50 m 48 m 80 m Cpter 10 Mesurement 63

21 MC Wi of te following is te orret wy to lulte te re of te trpezium sown? 1 A ì (3 + 5) ì 11 B 1 ì ( ) C 1 ì (11-3) ì 5 D 1 ì (11 + 5) ì 3 E 1 ì (3 + 11) ì 5 3 m 5 m 11 m UNDERSTANDING 3 A dress pttern ontins tese two piees. 30 m 30 m 60 m 3 m 60 m 47 m Find te totl re of mteril needed to mke ot piees. 4 A siene lortory s four enes wit te dimensions sown t rigt. Wt would e te ost of overing ll four enes wit protetive oting tt osts $38.50 per squre metre? 5 Stvros s epted ontrt to onrete nd edge te yrd, te dimensions of wi re sown in te figure t rigt. Wt will e te ost of onreting te yrd if onrete osts $8.00 per squre metre? Te yrd must e surrounded y edging strips, wi ost $8.5 per metre. Find: i te ost of te edging strips ii te totl ost of mterils for te jo. 6 Te side wll of tis sed is in te spe of trpezium nd s n re of 4.6 m. Find te perpendiulr distne etween te prllel sides if one side of te wll is.6 m ig nd te oter m ig..6 m 0.39 m 0.84 m.1 m 1.4 m 10 m 8.8 m m 9. m Digitl do WorkSHEET 10.1 do-3 7 MC Two trpeziums ve orresponding prllel sides of equl lengt. Te eigt of te first trpezium is twie s lrge s te eigt of te seond. Te re of te seond trpezium is: A twie te re of te first trpezium B lf te re of te first trpezium C qurter of te re of te first trpezium D four times te re of te first trpezium E impossile to sy REFLECTION Cn you tink of strtegy to elp you rememer te formul for finding te re of trpezium? 64 Mts Quest 8 for te Austrlin Curriulum

22 10F Volume of prisms nd oter solids Volume Volume is te mount of spe inside tree-dimensionl ojet. Volume is mesured in ui units su s mm 3, m 3 or m 3. Volume units n e onverted using te rt elow. ó 10 3 ó ó ui millimetres (mm 3 ) ui entimetres (m 3 ) ui metres (m 3 ) ui kilometres (km 3 ) ì 10 3 ì ì Prisms Prisms re solid spes wit identil opposite ends joined y strigt edges. Tey re treedimensionl ojets tt n e ut into identil slies, lled ross-setions. Prisms re nmed ording to te spe of teir ross-setion. Te ojets elow re ll prisms. Retngulr prism Hexgonl prism Tringulr prism Ojets tt do not ve uniform ross-setion n not e lssified s prisms. For exmple, te ojets elow re not prisms. Spere Cone Squre pyrmid Te volume of retngulr prism is given y te formul V = lw, were l is te lengt, w is te widt nd is te eigt of te prism. A retngulr prism n e ut to form two equl tringulr prisms. Te volume of ue is given y te formul V = l 3, were l is te side lengt of ue. Te volume of ny prism is given y te formul V = A ì H, were A is te ross-setionl re of prism nd H is te eigt of prism. Cpter 10 Mesurement 65

23 Te eigt of te prism is not neessrily te eigt of te ojet in true sense of te word. It is just te dimension perpendiulr to te ross-setion. Intertivity Volumes of prisms int-754 H A A V = A ì H Te se of tis prism is its ross-setion; H is te eigt of te prism. Te se of tis prism is not its ross-setion; H represents te dept (or lengt) of te prism. H Volume of solids wit uniform ross-setion tt re not prisms Te ojets wit uniform ross-setion, wose ends re not joined y strigt edges, n not e lssified s prisms. For exmple, te spes elow re not prisms, even toug tey ve uniform ross-setions. Te formul V = AH, were A is te ross-setionl re nd H is te dimension perpendiulr to it, will give te volume of ny solid wit uniform ross-setion, even if it is not prism. WORKED EXAMPLE 13 Find te volume of e of te following. 5 m 1 m 7 m 3 m 7 m 8 m A = 13 m THINK WRITE 1 Write te formul for te volume of te given spe. V = A ì H Identify te spe of te ross-setion nd, ene, write te formul to find its re A irle = p r 66 Mts Quest 8 for te Austrlin Curriulum

24 3 Stte te vlue of r. r = 3 4 Sustitute te vlue of r into te formul nd evlute. A = 3.14 ì 3 = 8.6 m 5 Stte te vlue of H. H = 5 6 To find te volume, multiply te ross-setionl re y te eigt nd inlude te orret units. V = 8.6 ì 5 = m 3 1 Write te formul for te volume of prism. V = A ì H Identify te spe of te ross-setion nd, ene, write te formul to find its re. 3 Stte te vlues of te vriles. (Note: is te eigt of te tringle, not of te prism.) 4 Sustitute te vlues of nd into te formul nd evlute. A tringle = 1 = 7, = 8 A = 1 ì 7 ì 8 = 8 m 5 Stte te vlue of H, te eigt of te prism. H = 1 6 To find te volume of te prism, multiply te rosssetionl re y te eigt nd inlude te orret units. V = 8 ì 1 = 336 m 3 1 Write te formul for te volume of te given spe. V = A ì H Stte te vlues of te ross-setionl re nd te eigt of te spe. 3 Multiply te ross-setionl re y te eigt nd inlude te orret units. A = 13, H = 7 V = 13 ì 7 = 91 m 3 REMEMBER ó 10 3 ó ó ui millimetres (mm 3 ) ui entimetres (m 3 ) ui metres (m 3 ) ui kilometres (km 3 ) ì 10 3 ì ì Volume is mesure of te mount of spe inside tree-dimensionl ojet.. Volume is mesured in ui units, su s ui entimetres (m 3 ) nd ui metres (m 3 ). 3. Prisms re solid spes wit identil opposite ends joined y strigt edges. Tey re tree-dimensionl figures wit identil lyers or ross-setions. 4. Te volume of prism is given y te formul V = A ì H, were A is te ross-setionl re nd H is te eigt of te prism ( dimension, perpendiulr to te ross-setion). 5. Use n re formul pproprite to e ojet to find te ross-setionl re. Cpter 10 Mesurement 67

25 EXERCISE 10F INDIVIDUAL PATHWAYS Volume of prisms nd oter solids FLUENCY 1 Wi of te tree-dimensionl spes elow re prisms? Ativity 10-F-1 Volume of prisms nd oter solids do-699 Ativity 10-F- More volume do-6930 Ativity 10-F-3 Cpity do-6931 d e Digitl do Spredseet Volume of prism do-34 WE 13 Find te volume of e of te following. 6 m 4.5 m 0 m A = 14 m A = 18 m 15 m d 40 m 5 m e 9 m 10.5 m f 13 m 9 m g i 8 m 4 m 6 m 8 m 8 m 10 m 7 m 6 m 5 m j k l 6 m 6 m 7 m.0 m 1.5 m.5 m 1.5 m 1.0 m 1.5 m 68 Mts Quest 8 for te Austrlin Curriulum

26 UNDERSTANDING 3 Wt volume of wter will retngulr swimming pool wit dimen sions sown in te potogrp elow old if it is ompletely filled? Te pool s no sllow or deep end. It is ll te sme dept..4 m 5 m 0 m 4 How mny ui metres of ement will e needed to mke te ylindril foundtion sown in te figure t rigt? 8 m 1. m 5 Wt re te volumes of tese piees of eese? 5 m 6 m 4. m 4 m 5.0 m 8.0 m 8 m 6 Wt is te volume of te red in sown t rigt? 9 m 18 m Cpter 10 Mesurement 69

27 7 How mu wter will tis pig troug, wit dimensions sown in te figure t rigt, old if it is ompletely filled? 30 m 15 m 55 m 15 m REASONING 8 Te res of te tree sides of retngulr ox re s sown in te figure. Wt is te volume of te ox? 70 m 150 m 180 m 10G 9 A vse is sped like retngulr prism wit squre se of lengt 11 m. It s litres of wter poured into it. To wt eigt does te wter re in te vse? (Hint: 1 litre = 1000 m 3.) Time Time n introdution Time is one of our most useful mesurements. We n use it to work out ow long we ve een doing someting, or ow long we ve until we must do someting. We n use it to mke future rrngements. Time is someting we ll use, every dy. Time is divided into units. Tere re: 60 seonds in 1 minute 60 minutes in 1 our 4 ours in 1 dy 7 dys in 1 week weeks in 1 fortnigt out 4 weeks in 1 mont 1 monts in 1 yer out 365 dys in 1 yer 10 yers in 1 dede 100 yers in 1 entury 1000 yers in 1 millennium. We lso use te word time to refer to n instnt (for exmple, 3 o lok) rter tn period. A lok or wt n disply te time in one of two wys. Some loks disply te time in nlogue form using our, minute nd seond nds tt move ontinuously s tey point to numers on te lok fe. Oter loks nd wtes disply set of digits tt nge in steps s time psses. REFLECTION How n you sy if solid s uniform ross-setion? 70 Mts Quest 8 for te Austrlin Curriulum