2 Measure the length of each line below to the nearest millimetre.

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2 E nglish immigrants wr in charg of building th first US railroads, so th US railroad gaug was basd on th gaug in England. Th English railways wr 1.44 mtrs (4 ft, 8.5 inchs) wid. Th qustion is, why wr th English railways 1.44 m? Th railway gaugs in England wr basd on th spacing ndd for wagons, which had to hav consistnt spacing to fit th ruts of th long distanc roads. Th first ruts in England wr mad by th ancint Roman war chariots. So why did th Romans choos 1.44 m for thir chariots whl width? Th war chariots whls wr st apart just far nough to accommodat th backsids of two horss! hi.com.au 229

3 Worksht R7.1 Worksht R7.2 Prpar for this chaptr by attmpting th following qustions. If you hav difficulty with a qustion, click on th Rplay Worksht icon on your Maths Zon CD or ask your tachr for th Rplay Worksht. 1 Calculat th following (b) (c) 6 4 (d) () (f) Masur th lngth of ach lin blow to th narst millimtr. (b) Worksht R7.3 3 Find th diffrnc in lngth btwn ach pair of lins to th narst millimtr. (b) Worksht R7.4 4 Masur th lngth and bradth of ach rctangl blow to th narst millimtr. (b) Worksht R7.5 5 Which of th shaps blow has th biggr ara? A B ara hctar masurmnt primtr bas hight mtr squar mtr bradth kilomtr mtric cntimtr lngth millimtr 230 MATHS ZONE 7

4 W can run into all sorts of problms if w havn t agrd on fixd units of lngth. A hand of salami plas. A hand of salami plas. In Australia, th mtric systm of masurmnt was introducd in Th systm usd in Australia bfor th introduction of th mtric systm was th imprial or British systm, which uss units such as inchs, ft, yards, mils, links, rods, chains and furlongs. In this systm it is awkward to convrt btwn th diffrnt units. Th mtric units of lngth usd most oftn ar: Th kilomtr (km) roughly qual to 3 laps of a sporting oval. Th mtr (m) about th lngth of an adult s strtchd pac. Th cntimtr (cm) roughly qual to th width of a littl fingr. Th millimtr (mm) th approximat thicknss of a mtal rulr. Most rulrs ar about 30 cm long, and show cntimtr and millimtr divisions. An imprial rulr Th mtric units of lngth ar rlatd as follows: 1 kilomtr = 1000 mtrs 1 mtr = 100 cntimtrs 1 cntimtr = 10 millimtrs You would masur somthing lik th distanc btwn two capital citis in kilomtrs, th lngth of a drivway in mtrs, th distanc around your waist in cntimtrs, and th thicknss of a pncil in millimtrs. 7 lngth, primtr and AREA 231

5 xrcis 7.1 Units of lngth Cor 1 Stat which mtric unit would b most appropriat for masuring: th lngth of your foot (b) th distanc from Sydny to Mlbourn (c) th hight of a footstool (d) th distanc around an athltics track () th lngth of a sho-lac (f) th distanc run in a marathon (g) th lngth of your bd 2 Choos th corrct answr. Th thicknss of a slic of brad would b bst masurd in: A mtrs B cntimtrs C millimtrs D kilomtrs (b) Th width of a studnt s dsk top would b bst masurd in: A mtrs B cntimtrs C millimtrs D kilomtrs (c) Which of th following givs th bst stimat of th distanc across a suburban strt? A 50 cm B 500 mm C 50 m D 5 m (d) Which of th following givs th bst stimat of th lngth of a mous s tail? A 1 cm B 10 cm C 100 cm D 1000 cm 3 Nam thr diffrnt objcts whos lngths should b masurd in mtrs. 4 Masur in cntimtrs th following lngths from th diagram of a modl aircraft shown blow. L E Prparation: Prp Zon Q2 D F hi.com.au Writ 5 cm 7 mm as 5.7 cm bcaus thr ar 10 millimtrs in a cntimtr. B J I G H A K C Th lngth of th aircraft (AB). (b) Th wingspan (CD). 232 MATHS ZONE 7

6 (c) Th bradth of a wing at its middl (EF). (d) Th lngth of th cockpit dom (GH). () Th lngth of th fuslag sction (IJ). (f) Th distanc from th front of th cockpit to th tip of th nos (HA). (g) Th tail width (LK). (h) Th distanc from th back of th wings to th nd of th tail (IB). Extnsion 5 Estimat th following. (b) Th lngth of this spd boat. (c) Th hight of this building. (d) 10 mm 1 m Th giraff s hight. Th lngth of th btl. 6 Guss th answr to ach of th following thn us your rulr to hlp you dcid. Which horizontal lin is longr? A B 7 lngth, primtr and AREA 233

7 (b) Which diagram has th largr (c) Is th hat shown blow cntral circl? as wid as it is tall? A B (d) Which prson is th tallst? C 7 Explain ach illusion or ffct in Qustion 6 and why you think it happns. A B Worksht A7.1 Th as with which w can convrt btwn units is th grat advantag of th mtric systm. Convrting btwn mtric units of lngth is mad asy bcaus w only vr nd to multiply or divid by 10, 100, 1000 tc. to chang to diffrnt units. This is don by simply moving th dcimal point in th valu bing convrtd. Convrting btwn mtric units is mad asir still by using th dcimal point movmnt chart on th following pag. Rmmbr, mov th dcimal point right on plac for vry zro whn multiplying by 10 or 100 or 1000 tc., and mov th dcimal point lft whn dividing. 234 MATHS ZONE 7

8 km m cm mm Rmmbr that whn you convrt largr units to smallr ons, your answr must b biggr. For xampl, convrting km to m: 2 km = 2000 m workd xampl 1 Convrt: 62 km to m (b) 875 cm to km Stps 1. Writ 62 km as 62.0 km. 2. Plac your fingr on km on th chart abov and mov it to m. Not how many placs and in which dirction you movd. (3 placs to th right.) Solutions 3. Now mov th dcimal point 3 placs to th right also, i.. multiply by km 4. Fill in th spacs with zros. = m (b) 1. This convrsion rquirs a dcimal point (b) movmnt of 5 placs to th lft, i.. divid by Fill in th spacs with zros, and plac a zro in th units plac to mphasis th placmnt of th dcimal point cm = km Sinc th dcimal point nds up at th right-hand nd of a whol numbr, thr is no nd to show it. xrcis 7.2 Convrting units of lngth Cor Prparation: Prp Zon Q1 1 Copy and complt th following convrsions. 5 km = m (b) 23 km = m (c) 20 km = m (d) 3.6 km = m () 9.7 km = m (f) 10.6 km = m Worksht C7.1 7 lngth, primtr and AREA 235

9 (g) 0.2 km = m (h) 0.03 km = m (i) km = m (j) 700 m = cm (k) 9 m = cm (l) 65 m = cm (m) 3 m = cm (n) 0.55 m = cm (o) 5.6 m = cm (p) 4 cm = mm (q) 12 cm = mm (r) 80 cm = mm (s) 17.2 cm = mm (t) 2.9 cm = mm (u) 20.4 cm = mm 2 Copy and complt: 4.7 km = cm (b) 9.05 km = cm (c) km = cm (d) 0.7 km = mm () km = mm (f) km = mm (g) 4.95 m = mm (h) 3.2 m = mm 3 Copy and complt th following convrsions. 61 mm = cm (b) 20 mm = cm (c) 104 mm = cm (d) 42.3 mm = cm () mm = cm (f) 30.9 mm = cm (g) 0.9 mm = cm (h) 0.07 mm = cm (i) 0.1 mm = cm (j) 800 cm = m (k) 1200 cm = m (l) 90 cm = m (m) 86 cm = m (n) 712 cm = m (o) 3 cm = m (p) 2000 m = km (q) 4200 m = km (r) 8097 m = km (s) 9 m = km (t) 50 m = km 4 Copy and complt th following convrsions. 560 mm = m (b) 2400 mm = m (c) 97 mm = m (d) 9000 cm = km () cm = km (f) 567 cm = km (g) mm = km (h) 7800 mm = km 5 Copy and complt th following convrsions m = cm (b) 289 mm = cm (c) 4567 m = km (d) 700 km = m () 8.7 cm = mm (f) 30.9 cm = m (g) mm = km (h) 0.63 m = mm (i) 830 mm = m (j) 780 cm = km (k) 1.92 km = cm (l) km = mm 6 Choos th corrct answr. 5.9 km is qual to: A m B m C 5900 m D m (b) 670 cm is qual to: A 0.67 m B 6.7 m C 670 m D 6.7 km 7 What do th prfixs milli, cnti and kilo man? 8 A snow gum in th Snowy Mountains was masurd to b 2976 cm. How many mtrs is this? 236 MATHS ZONE 7

10 9 In 1937, a giant arthworm in South Africa was masurd to b 6.7 m in lngth. Writ this lngth in cntimtrs. Som Australian arthworms 10 Th bird-ating spidr of South Amrica has a body lngth of 89 mm and a lg-span of 254 mm. Writ ths masurmnts in cntimtrs. 11 Th dinosaur Tyrannosaurus rx is thought to hav bn 548 cm high and 1433 cm long. Convrt ths dimnsions to mtrs. Extnsion 12 Giv two lngths in mtrs that ar lss than 3 cm. 7 lngth, primtr and AREA 237

11 13 Andrw walkd 850 m from his hom to th school gats, thn anothr 220 m to his classroom. What is th total distanc in mtrs that h walkd to his classroom? What is this distanc in kilomtrs? 14 Clair is building a dsk and sh wants it to b wid nough that sh can fit th lngth of two A4 shts across it. If th lngth of an A4 sht is 298 mm, how wid dos Clair s dsk hav to b in millimtrs? What is this lngth in cntimtrs? 15 Th following ar som mistaks mad by a class whn doing convrsions. For ach, xplain what mistak has bn mad and writ th corrct answr. 27 m = 0.27 cm (b) 765 mm = 7.65 cm (c) 3800 m = 3.08 km (d) 0.8 km = m () 54 cm = 504 mm (f) 1356 cm = m Many situations involv lngths masurd in diffrnt units. It is ssntial that all lngths b xprssd in th sam units bfor prforming any oprations, such as adding or subtracting. As a gnral rul, w usually convrt to th smallr unit so that whol numbrs ar involvd. Put all lngths in th sam units bfor adding or subtracting. workd xampl 2 Add ach of th following pairs of lngths, giving your answr in th units in brackts cm and 250 mm (mm) (b) 420 m and 2.8 km (m) Stps Solutions 1. Convrt to th unit indicatd in brackts cm = = 124 mm 2. Add th valus togthr and stat th answr = 374 mm (b) 1. Convrt to th unit indicatd in brackts. (b) 2.8 km = = 2800 m 2. Add th valus togthr and stat th answr = 3220 m 238 MATHS ZONE 7

12 xrcis 7.3 Using mtric units of lngth Prparation: Prp Zon Q1 and 3, Ex 7.2 Cor 1 Add ach of th following lngths, giving your answr in th units statd in brackts cm and 870 mm (mm) (b) 560 m and 3.1 km (m) (c) 3.54 m and 56.3 cm (m) (d) 2100 mm and 7.9 m (mm) () cm and km (km) (f) 2.08 m and 597 cm (cm) (g) 5900 mm and 2.3 km (m) (h) 25 m and mm (cm) (i) 1080 cm and mm (m) (j) m and cm (km) 2 Choos th corrct answr. Th total lngth obtaind whn 2.5 m and 43 cm ar addd is qual to: A 45.5 m B 45.5 cm C 293 cm D 293 m (b) Th total distanc travlld by an athlt who cycls 6 km thn runs 800 m is: A 806 m B 608 m C 14 km D 6800 m 3 Find th diffrnc btwn ach of th following pairs of lngths, xprssing your answr in th units statd in brackts m and 0.54 km (km) (b) 5.02 m and 78.5 cm (m) (c) 780 mm and 5.8 cm (cm) (d) 55.6 cm and 430 mm (mm) () 5200 cm and mm (m) (f) 6.8 m and 2900 mm (cm) (g) 2870 m and 6000 cm (km) (h) cm and km (m) 4 Writ two lngths in mtrs that hav a diffrnc of 6 cm. 5 A paintr can rach a hight of 2.8 m whn hr ft ar on th ground. How high could sh rach standing on a 72 cm high chair? (Answr in mtrs.) 6 To rpair damag to a fnc, Horac rquirs pics of railing timbr 2.5 m, 3.7 m and 925 mm long. What total lngth (in mtrs) dos h nd? 7 Cordlia s racing car braks down only 230 m from th finish of a 25 km rac. What distanc did sh complt bfor this tragdy? (Answr in kilomtrs.) 8 A photo 127 mm long is to b put in a fram 9.6 cm long. How many millimtrs must b trimmd from th photo? Animation Extnsion 9 A bricki stacks som lftovr bricks bhind a garag. H finds that in ordr to fit thm in th spac availabl, h must mak a pil 14 bricks high. If ach brick is 74 mm high, how many mtrs up th garag wall dos th stack rach? 7 lngth, primtr and AREA 239

13 10 A buildr ordrs 60 pickts for a fnc. If ach pickt is 183 cm long, and th wood costs 95 cnts pr mtr, how much dos th ordr cost? 11 A grocr builds a display of cral boxs 8 boxs high. If ach box is 33 cm tall, how many mtrs high is th display? 12 A slpr wall is constructd 150 mm as shown. If ach slpr is 150 mm wid, how tall is th wall in mtrs? 13 An accountant is assurd by hr stationry supplir that th pncils sh has bought will writ for at last 600 mtrs ach. If sh bought a packt of 12 pncils, how many kilomtrs can sh look forward to writing with thm? 14 Paula gos jogging around a narby track at vry opportunity, and on day manags to jog around th track a total of 17 tims. If th track is 470 m around, how many kilomtrs did sh jog this day? 15 Laurn is prparing som shasliks for a barbcu. Sh wishs to plac pics of marinatd mat 4 cm long on 30 cm bamboo skwrs, laving 3 cm of skwr fr at ach nd. How many pics of mat will sh b abl to plac on ach skwr? Ralph s rulrs Ralph is planning a woodwork modl and nds to draw a lin 6 cm long. H has bn using as rulrs 2 straight pics of wood with no markings, but h knows thir lngths ar 10 cm and 8 cm. How can h us ths pics of wood to masur a 6 cm lin? Act it out. 240 MATHS ZONE 7

14 Primtr is a trm usd to dscrib th boundary of an objct or ara. A hocky fild has a whit boundary lin markd along its primtr. A fram gos around th primtr of a pictur. A cushiond wall forms th primtr of a billiard tabl. Primtr is th distanc around th outsid of a shap. xrcis 7.4 Primtr Tutorial Prparation: Prp Zon Q1 and 4, Exs 7.2 and 7.3 Cor 1 Find th primtr of ach of th following rctangls. (Th dots ar 0.5 cm apart vrtically and horizontally.) (b) (c) (d) () (f) 2 Can you find a shortcut mthod for calculating th primtr of a squar or rctangl? If so, dscrib your mthod/s. 7 lngth, primtr and AREA 241

15 3 Choos th corrct answr. Th primtr of th rctangl is: A 13 cm 7 cm B 20 C 40 cm D 91 cm 4 Find th primtr of ach of th following rctangls. (b) 2 cm 13 cm 6 cm 3 cm 8 cm (c) (d) () 4 cm 7 cm 8 cm 6 cm 60 mm 4 mm (f) (g) (h) 30 mm 25 m 15 m 13 mm 25 m 15 m 5 Find th primtr of ach shap on th half-cntimtr dot grid blow. (b) (c) (d) 242 MATHS ZONE 7

16 6 Masur th lngths of th sids of th shaps blow and calculat thir primtrs to th narst cm. (b) (c) (d) () (f) (g) (h) 7 Convrt ach sid lngth to th sam units and calculat th primtr of ach of th following. (b) 4 cm 50 mm Convrt to th smallr unit in ach cas. 4 cm 30 mm 6 cm 50 mm 7 lngth, primtr and AREA 243

17 (c) 26 mm (d) 72 mm 3.1 cm 4.6 cm 4.2 cm 5.3 cm () (f) 2 cm 19 mm 41 mm 5 cm (g) 90 cm 60 cm 1 m 60 cm 0.8 m (h) 2 m 95 cm 140 cm 1.2 m (i) 1.5 km 800 m (j) 1.3 km 1400 m 2.5 km 1200 m 1700 m 2 km 0.7 km 8 Each figur blow has on or mor sid lngths missing. Find th primtr of ach on. (b) 4 m 8 cm Worksht C7.2 7 m 6 cm 8 cm In this qustion, all angls ar right angls. 14 m 2 m 12 cm 244 MATHS ZONE 7

18 (c) 4 cm (d) 23 mm 14 mm 7 mm 5 cm 5 cm 3 cm 1 cm 8 mm 19 mm 8 mm 1 cm 9 Find th primtr of a rctangl of lngth 67 mm and width 23 mm. 10 Find th primtr of a squar whos sids masur 55 m. Extnsion 11 Th lngth and bradth of a rctangl ar both whol numbrs in cntimtrs. Writ down possibl dimnsions if its primtr is 84 cm. 12 Find th sid lngth of a squar with a primtr of 36 cm. 13 Find th bradth of a rctangl with a primtr of 32 cm and a lngth of 10 cm. 14 A ntball court masurs 30.5 m by m. Calculat its primtr. 15 A yacht sails thr straight lgs of a cours which form a triangl. Th lngth of th lgs ar 2.5 km, 1.7 km and 3.9 km. What distanc dos th yacht sail to complt th cours? 16 A group of phys. d. studnts run around th primtr of a court in thir gymnasium which is rctangular and has dimnsions 38 m by 16 m. What distanc will thy run if thy complt 6 laps? 17 Bob wishs to run two strands of 40 m wir around his proprty to mark 95 m its boundary. A plan of th proprty is shown opposit. If h 43 m can obtain th ncssary wir for 30 m 60 cnts pr mtr, how much 112 m will th wir cost him? 18 Th local swimming pool is rctangular, of dimnsions 25 m by 12 m. If it has a 1 m wid path around its primtr, what is th distanc around th outr dg of th path? Qustions Worksht A7.2 Homwork lngth, primtr and AREA 245

19 Answr th following, showing your working, and thn arrang th lttrs in th ordr shown by th corrsponding answrs to find th cartoon caption. Find ach lngth in mtrs. 120 cm E km I 18 cm m R 1.6 m cm N km 4800 mm C 1280 mm 36 cm A Th primtr of a rctangl masuring 1.2 m by 0.9 m M Th primtr of a rctangl masuring 36 cm by 82 cm T Th primtr of a squar of sid lngth 35 cm. E Th sid lngth of a squar with primtr 8.4 m. E Th longr sid of a rctangl that has a primtr of T 4.6 m and on sid of lngth 1 m MATHS ZONE 7

20 Using our xampl of a billiard tabl again (pag 241), th grn cloth surfac that th billiard ball rolls around on rprsnts th ara of th tabl. Ara is th amount of spac containd by a plan (flat) shap. Ara may b masurd in squar millimtrs (mm 2 ), squar cntimtrs (cm 2 ), squar mtrs (m 2 ), squar kilomtrs (km 2 ) or hctars (ha). A squar millimtr (actual siz) A squar cntimtr (actual siz) 1 m 1 m A squar mtr A squar kilomtr A hctar is in btwn a squar mtr and a squar kilomtr. 1 ha = m 2 Whn w find th ara of somthing w ar stating how many squars fit into th ara. For xampl, if th front covr of a book has an ara of 160 cm 2, this mans that 160 squar cntimtrs can fit onto th front covr of th book. Convrting aras is diffrnt to convrting lngths. On squar cntimtr is not qual to tn squar millimtrs. You nd to imagin how many squars with a sid lngth of on millimtr fit insid a squar with a sid lngth of on cntimtr. Thr ar 100 (10 rows of 10). This is shown undr th magnifying glass on th following pag. 7 lngth, primtr and AREA 247

21 1 cm 10 mm 1 cm 10 mm To convrt units of ara, us th following hlpful summary km 2 ha m 2 cm 2 mm Whn finding aras, it is oftn asir to convrt th units first, thn do th calculations. xrcis 7.5 Ara Prparation: Prp Zon Q5, Exs 7.2 and 7.4 Cor 1 Stat which of th units of ara mm 2, cm 2, m 2 or km 2 would b most suitabl for masuring th ara of: a sht of writing papr (b) your littl to-nail (c) th city of Hobart (d) a pizza () a hous block (f) Stadium Australia at Sydny Olympic Park (g) Nw South Wals (h) a small watch fac (i) a sht of nwspapr (j) th floor of a classroom 2 Copy and complt th following convrsions. 5 m 2 = cm 2 (b) 12 ha = m 2 (c) 94 cm 2 = mm 2 (d) cm 2 = mm 2 () m 2 = cm 2 (f) ha = m 2 Intractiv 248 MATHS ZONE 7

22 (g) m 2 = ha (h) 9800 mm 2 = cm 2 (i) cm 2 = m 2 (j) 950 cm 2 = m 2 (k) 23.6 ha = km 2 (l) 3400 m 2 = ha (m) 460 cm 2 = m 2 (n) 345 cm 2 = mm 2 (o) m 2 = ha (p) 5570 ha = km 2 (q) m 2 = cm 2 (r) 98.6 mm 2 = cm 2 3 Th following aras hav bn drawn on cntimtr grid papr. Find th total numbr of cm 2 in ach on. (b) (c) (d) () Do not includ th shadd ara. (f) Do not includ th shadd ara. 7 lngth, primtr and AREA 249

23 (g) (h) (i) (j) 4 Choos th corrct answr. A rctangl that has thr rows ach of four squar cntimtrs has an ara of: A 7 cm 2 B 12 cm 2 C 14 cm 2 D 24 cm 2 5 Th following aras hav bn drawn on cntimtr grid papr. Find th shadd ara in ach cas. (b) 250 MATHS ZONE 7

24 (c) (d) 6 Th following aras hav bn drawn on cntimtr grid papr. Find (i) th primtr and (ii) th ara of ach on. (b) (c) (d) 7 lngth, primtr and AREA 251

25 () (f) Extnsion 7 Th following odd shaps hav bn drawn on cntimtr grid papr. Estimat th ara of ach shap. (b) 8 Estimat th ara of th following, using appropriat units. your classroom floor (b) your school grounds (c) th suburb your school is in (d) Australia () a standard postag stamp (f) th front covr of this txtbook Qustions 252 MATHS ZONE 7

26 Rmoving matchsticks Starting with th arrangmnt of matchsticks shown, how could you: rmov 4 matchs to lav 5 idntical squars (b) rmov 8 matchs and lav 4 idntical squars (c) rmov 6 matchs to lav 3 diffrnt squars? Us your imagination. You ll gt it in th nd. How many squars on a chssboard? Bfor trying to answr this qustion, first considr a 3 3 squar board. This grid contains: nin 1 1 squars four 2 2 squars and on 3 3 squar making a total of 14 squars. For th following qustions you may lik to work in pairs to mak sur all squars ar countd. 1 How many squars ar thr in ach of th following grids? (b) (c) (d) 7 lngth, primtr and AREA 253

27 2 Copy and complt th following tabl for squar grids. Grid Numbr of squars Can you dtrmin th numbr of squars in a chssboard (an 8 8 grid)? Considr a rctangl of lngth 6 cm and bradth 3 cm. Th rctangl contains 3 rows of 6 squars, so its ara is qual to 3 cm 6 cm = 18 cm 2. W could also hav calculatd 6 cm 3 cm = 18 cm 2. In othr words, th ara of a rctangl is qual to its lngth multiplid by its bradth. Using th pronumrals A for ara, l for lngth and b for bradth, A = l b or mor simply, A = lb This is th formula for ara of a rctangl. workd xampl 3 Find th ara of ach of th following shaps. 7 cm (b) 3 cm (c) 2 cm 5 cm 5 cm 5 cm 3 cm 6 cm 10 cm 254 MATHS ZONE 7

28 Stps Solutions 1. Writ down th formula for th ara of a A = lb rctangl. 2. Substitut th valu 7 for l and 5 for b. A = Calculat th rsult. A = 35 cm 2 (b) 1. Divid th composit shap into rctangls. This may b don in diffrnt ways. (b) 3 cm Ara 1 2 cm Ara 2 3 cm 2. Calculat th ara of ach part. Ara 1 = 3 2 = 6 cm 2 Ara 2 = 6 3 = 18 cm 2 3. Add th aras. Total ara = 24 cm 2 (c) 1. Imagin a rctangl containing th (c) triangl. 5 cm 6 cm 2. Calculat th ara of this rctangl. A = lb A = 5 10 A = 50 cm 2 10 cm 3. Halv to gt th ara of th triangl. A = 50 2 Ara rquird = 25 cm 2 Ara of a rctangl: A = lb l b Tutorial 7 lngth, primtr and AREA 255

29 xrcis 7.6 Ara of a rctangl Prparation: Prp Zon Q1 and 5, Exs 7.4 and 7.5 Cor 1 Calculat th aras of th following rctangls drawn on cntimtr grids. (b) (c) (d) () (f) 2 Choos th corrct answr. Th ara of th following rctangl is: A 14 cm 2 B 28 cm 2 C 33 cm 2 D 66 cm 2 3 cm 11 cm 3 Find th aras of th following rctangls. (b) (c) 9 cm 3 cm 6 cm 4 cm (d) 2 cm () (f) 10 cm 9 mm 6 cm Worksht C cm 12 m 10 mm 3 m 256 MATHS ZONE 7

30 (g) (h) (i) 5 km 16 km 4.5 cm 2 cm 6.3 cm 4 Sinc th bradth of a squar is th sam as its lngth, th formula for th ara of a squar is A = l l or simply A = l 2.Us this formula to find th ara of ach of th following squars. (b) 3 cm 1 cm 1 cm (c) (d) () 12 mm 6 cm 7 cm 12 mm 6 cm 7 cm (f) (g) (h) 2.5 km 3.6 m 9 cm 2.5 km 3.6 m 9 cm 7 lngth, primtr and AREA 257

31 5 Find th ara of ach of th following triangls by first considring a rctangl. (b) Worksht C7.4 5 cm 6 cm 8 cm 12 cm (c) (d) 5 cm 6 cm 9 cm 7 cm () (f) 4 cm 12 cm 7 cm 8 cm 6 Dtrmin th ara of ach shadd rgion. All angls ar right angls. 1 cm (b) 3 cm 8 cm 5 cm 13 cm 2 cm Worksht C7.5 2 cm 4 cm 2 cm 2 cm 4 cm (c) 3 cm 1 cm 4 cm (d) 3 cm 7 cm 2 cm 11 cm 7 cm 8 cm 15 cm 258 MATHS ZONE 7

32 9 mm () 5 mm 5 mm (f) 4 m 1 m 3 m 13 mm 3 mm 8 m 7 m 7 mm 10 m (g) (h) Worksht C7.6 2 cm 2 cm 7 cm 11 cm 12 cm 7 cm 3 cm 10 cm 7 Find (i) th primtr and (ii) th ara of ach shap blow. All angls ar right angls. 9 km (b) (c) 5 km 13 m 16 cm (d) 5 m 5 cm 25 cm 4 cm () 7 m (f) 10 cm 8 m 4 m 6 cm 6 cm 12 m 3 cm 6 m 3 cm 3 cm 15 cm 8 m 7 lngth, primtr and AREA 259

33 8 Find th ara of a rctangl of lngth 32 cm and bradth 9 cm. 9 Find th ara in km 2 of a rctangl of lngth 3 km and bradth 800 m. 10 What is th ara in cm 2 of a rctangl of lngth 450 mm and bradth 70 cm? 11 Find th primtr and ara of a squar whos sids masur 5.6 cm. 12 Writ down th possibl dimnsions of a rctangl with an ara of 24 cm 2. (b) Do all rctangls with an ara of 24 cm 2 hav th sam primtr? Explain. 13 Find th bradth of a rctangl with lngth 7 cm and ara 28 cm Find th lngth of a rctangl with bradth 2.6 m and ara m 2. Extnsion 15 Olga wishs to covr a tabl-top that is 2.4 m long and 1.2 m wid with laminx. Find th ara of laminx sh will rquir, in cm 2. (b) What lngth strip dos sh nd to purchas to go around th sids of th tabl-top? 16 Tricia has obtaind a quot of $21 pr squar mtr for hr drivway to b r-surfacd. If hr drivway is rctangular and masurs 12 m long and 3.2 m wid, what will th job cost hr at th rat quotd? 17 Guy wishs to grass a rctangular sction of his yard which is 8.5 m long and 6.9 m wid. How many grams of sd will h nd to us if th rcommndd sd covrag is 60 grams pr squar mtr? (b) What lngth of wood would Guy nd to purchas to crat a timbr surround for th sction? 18 Trry is having a doorway put in on of th walls in his hous. If th wall is 5 m long and 2.4 m high and th doorway masurs 2 m by 0.82 m, what ara of wall will rmain aftr th doorway is compltd? (b) Th architravs go along th sids and top of th doorway. What lngth of architravs is ndd? 19 A buildr wishs to stimat th numbr of bricks rquird to build a wall 4.2 m wid and 2.6 m high. If 1 squar mtr of brick wall contains 48 bricks, how many ar ndd? 260 MATHS ZONE 7

34 20 What is th primtr of a rctangl of ara 20 cm 2 and bradth 2 cm? (b) Is this primtr th sam as for a rctangl of th sam ara but with a bradth of 4 cm? 21 Find th ara of th triangular sail shown. 2.1 m 1.6 m 22 Find th wing ara of th papr plan. 8 cm 20 cm 8 cm 23 Find th ara of th farm using th plan providd. (b) What lngth of fncing is ndd to go around th outsid of th proprty? 600 m 500 m 250 m 100 m 400 m 300 m 24 Kasia wants to covr both sids of a postr with clar contact adhsiv. If th postr masurs 63 cm by 87 cm, what ara of covring will sh nd if sh wishs to ovrlap th postr by 5 cm all around? 25 How many squar Animation cntimtrs of cardboard ar ndd to construct a cub of dg lngth 9 cm? 9 cm 9 cm 9 cm Worksht C7.7 hi.com.au Qustions Worksht T7.1 Worksht A7.3 Worksht A7.4 7 lngth, primtr and AREA 261

35 W hav sn that th ara of a rightangld triangl is qual to half th ara of a rctangl. Th ara of any triangl can b shown to b qual to half th ara of a rctangl of th sam bas lngth and hight. Th ara of th rctangl shown is b h or bh (b = bas lngth, h = hight), so th ara of th triangl is givn by: h b A = 1 2 -bh Not also that th hight masurmnt is prpndicular, i.. at 90 to th bas masurmnt. It rprsnts th biggst possibl vrtical masurmnt btwn th top of th triangl and th bas, or its xtnsion. workd xampl 4 Find th ara of th following triangls. (b) 3 m 12 cm 17 m 23 cm Stps Solutions 1 1. Writ down th formula for ara of a triangl. A = --bh Substitut in th valus b = 23 and h = 12. A = Evaluat. A = 138 cm 2 1 (b) 1. Writ down th formula. (b) A = --bh Substitut in th valus 17 for b and 3 for h. A = Evaluat. A = 25.5 m MATHS ZONE 7

36 Whn calculating ara, you may b askd to giv your answr in units diffrnt from th ons givn in th qustion or thr may b mixd units in th qustion. In both cass, you nd to convrt your original valus to th rquird units first, thn calculat th ara using th appropriat formula. workd xampl 5 Find th ara of th following triangl in m cm 120 cm Stps Solution 1 1. Writ down th formula for ara of a triangl. A = --bh 2 2. Convrt b and h valus into mtrs. b = 1.2 m h = 0.6 m 1 3. Substitut b = 1.2 and h = 0.6 into th formula. A = Evaluat. A = 0.36 m 2 Tutorial xrcis 7.7 Ara of a triangl Cor 1 Calculat th ara of ach triangl blow. (b) Prparation: Prp Zon Q1 and 5, Exs 7.5 and cm 6 m 12 cm 14 m (c) (d) 7 mm 12 cm 10 mm 19 cm 7 lngth, primtr and AREA 263

37 () (f) 5 m 9 m 7 cm 13 cm (g) 22 mm (h) 10 m 8 mm 36 m (i) 12 cm (j) 8.3 cm 9.6 mm 4 mm (k) 2.4 cm 6.7 cm (l) 5.6 cm 12.1 cm 2 Choos th corrct answr. In th diagram, th hight of th triangl is: A 3 cm B 4 cm C 7 cm D 9 cm (b) Th bas lngth of th triangl is: A 21 mm B 31 mm C 42 mm D 59 mm (c) Th ara of th triangl shown is: A 14 cm 2 B 24 cm 2 C 28 cm 2 D 48 cm 2 4 cm 7 cm 3 cm 9 cm 59 mm 21 mm 31 mm 42 mm 6 cm 8 cm 264 MATHS ZONE 7

38 3 A triangl has an ara of 36 cm 2. Giv two possibl combinations for th triangl s bas lngth and hight. 4 Find th total sail ara for this yacht. 1.6 m 1.4 m 2.6 m 2.8 m 5 Find th ara of papr rquird to build th kit shown. Giv your answr in m 2. 6 Find th ara of sht mtal rquird for this road sign in m cm 70 cm 20 cm CHICKENS CROSSING 60 cm 70 cm 7 Find th total ara of th four qual facs of th containr of frozn drink (a Ttrapak) shown. 8 Th labl on a tin of paint claims th contnts will coat 4 squar mtrs. How many tins would b ndd to paint th triangular gabl picturd? 8.1 cm ICY BLOCKO 4.8 m 10 cm 5 m 7 lngth, primtr and AREA 265

39 9 Find th ara of ach of th following composit shaps. (b) 11 cm 10 cm 7 cm 12 cm 6 cm 6 cm 15 cm (c) 20 cm (d) 9 cm 10 cm 18 cm 18 cm 10 cm 6 cm () (f) 5.5 cm 3 cm 10 cm 16.2 cm 10 cm 2 cm 21.5 cm 8.2 cm Qustions Homwork 7.2 Do ths in your had as quickly as you can Tim targt: 2 minuts and writ down th answrs of $ $2.50 plus 78 cnts 8 What is th scond largst factor of 64? 9 Tak 19 from th product of 12 and What tim is it thr and a quartr hours aftr a.m.? MATHS ZONE 7

40 Print finishr: Vicki Standing Company: Canbrra Prss Qualifications/Exprinc: fiv yars as bindry assistant; thr yars of trad school; fouryar apprnticship Rlatd occupations: bindr, printr, typsttr In my job, my dutis includ undrstanding what a book or publication is supposd to look lik and th stting up of machinry for such tasks as cutting papr with a guillotin, folding, collating and binding books basically vrything that happns aftr somthing has bn printd. I m rsponsibl for th quality of th work, and tim dadlins, and for dircting th machin assistants. I chos this job aftr prvious carrs as a book-kpr and a bank mploy bcaus I was looking for an intrsting challng at work with th chanc of futur opportunitis. My favourit part of mathmatics at school was achiving th corrct answr whn doing algbra. Maths was vry important in my arlir carrs and is also important in my currnt on. I us maths for tasks lik nsuring th right amount of matrial is usd, stimating how long diffrnt parts of production tak, maximising th numbr of pags to b cut from a larg sht, and calculating pay rats and ovrtim loading at th nd of a pay wk. Th print finishr s problm Printrs buy shts of papr in larg standard sizs. On of th most common standard sizs is 760 mm 1020 mm. Vicki has to work out which way to cut ths shts so that sh gts th maximum numbr of A5 shts. A5 shts ar 210 mm 148 mm. To do this, sh dos th following calculations: = = = = = = 20 7 lngth, primtr and AREA 267

41 This tabl shows that cutting th A5 shts out of th larg shts vrtically givs 18 A5 shts pr larg sht, whil cutting thm horizontally givs 20 A5 shts pr larg sht. This mans that th bttr way to cut is horizontally. Th following guillotin diagram shows th A5 shts bing cut vrtically. Th shadd parts rprsnt th xcss papr and ar calld offcuts mm 210 mm 760 mm 148 mm This guillotin diagram shows th A5 shts bing cut horizontally mm 210 mm 760 mm 148 mm 1 What dos th numbr aftr th dcimal point in th tabl tll us? 2 Why do w round 6.8 to 6 and not 7 for this sort of problm? 3 Vicki has to cut A4 (210 mm 297 mm) shts from a standard larg sht (760 mm 1020 mm). Draw a tabl and two guillotin diagrams to find out th maximum numbr of A4 shts that can b cut out. 4 If Vicki nds 4000 A4 shts, how many larg shts will sh nd to cut to gt this many? 5 Vicki has workd out a way of cutting ight shts of siz 370 mm 250 mm from on standard larg sht of papr of siz 760 mm 1020 mm. Can you work out how sh did it? Draw a guillotin diagram to hlp you. 268 MATHS ZONE 7

42 Summary Copy and complt th following summary of this chaptr using th words and phrass from th list. A word or phras may b usd mor than onc. 1 is th distanc around th outsid of a shap. 2 To calculat th of a rctangl, you multiply th by th bradth. 3 Thr ar 1000 millimtrs in a. 4 Thr ar in a kilomtr. 5 Th ara of a rctangl that masurs 3 m by 2 m is 6. 6 Th ara of a triangl is half th tims th squar mtrs is quivalnt to on. Qustions 1 Writ th units of lngth from th abov ky words in ordr from largst to smallst. 2 Writ in words what is mant by cm 2, m 2 and km 2. 3 Thr ar 100 cntimtrs in a mtr. Find two othr words that start with cnt and writ thir manings. 4 Dscrib a ral-lif situation whr it is ncssary to calculat a primtr. 5 Dscrib a ral-lif situation whr it is ncssary to calculat an ara. 6 Mak at last fiv words of at last thr lttrs from th lttrs in th grid. All words T E R must includ th middl lttr. Can you P E I find th word that uss all nin lttrs? 7 Th word lngth is a noun. Writ a vrb and an adjctiv that com from th word lngth. M E R Ky words ara bas bradth cntimtrs hctar hight kilomtr lngth masurmnt mtr mtric millimtr primtr squar mtrs Worksht L7.1 Worksht L7.2 7 lngth, primtr and AREA 269

43 FAQs I can't rmmbr whn to divid and whn to multiply whn convrting units. Is thr an asy way to rmmbr this? Just think logically about it. Whn convrting from cntimtrs to mtrs, for xampl, think that bcaus mtrs ar biggr than cntimtrs w nd lss of thm. So this mans you will nd to divid. To go from kilomtrs to millimtrs you nd to multiply bcaus you nd mor millimtrs, bcaus thy ar smallr. Cor 1 Choos th corrct answr in ach cas. Th lngth of a papr clip is approximatly: A 3 mm B 3 cm C 0.3 m D 300 mm (b) Th hight of an avrag hous ciling is roughly: A 260 mm B 0.26 km C km D 2.6 m 2 Copy and complt th following lngth convrsions km = m (b) cm = km (c) 9.2 m = mm (d) 42 m = cm () 980 m = km (f) km = mm (g) cm = m (h) 8.52 cm = m (i) 609 mm = cm (j) 6700 m = km 3 Add th following lngths, giving your answr in th units statd in brackts cm and 540 mm (cm) (b) 340 m and 2.7 km (m) (c) cm and 0.62 km (km) (d) 2.78 cm and 30 mm (mm) 4 Gram dcids to start jogging ach day and bgins on day by jogging 1 km. If h incrass th distanc h jogs by 600 m ach day, how far will h hav joggd altogthr aftr 4 days? 5 Find th primtr of ach of th following shaps. (b) 19 cm (c) 32 cm 14 cm 3.5 cm 46 mm (answr in mm) cm 270 MATHS ZONE 7

44 (d) () (f) 59 mm 47 mm 6.5 m 13 cm 9 cm 5.5 m 6 cm 3 m (answr in cm) 1.5 m 12 m 5 m 18 cm 5 cm 4 cm 6 Find th primtr of a squash court 9.75 m long and 6.4 m wid. 7 Copy and complt th following ara convrsions. 4.2 cm 2 = mm 2 (b) m 2 = ha (c) cm 2 = m 2 (d) 528 ha = km 2 () 80.7 ha = m 2 (f) m 2 = cm 2 8 Find th ara of ach figur blow in th units indicatd in brackts. (m 2 ) (b) (cm 2 ) m 8 m 14 mm (c) (mm 2 ) 17 cm (d) (cm 2 ) 8 cm 13 cm 12 cm 9 Find th ara of th following triangls. (b) 13 cm 6 cm 6 cm 12 cm 5 cm 4 cm lngth, primtr and AREA 271

45 Extnsion 10 Find th ara of ach figur. 7.6 (b) 5 cm 2 m 5 m 2 m 7 cm 2 cm 4 cm 2 m 3 m 3 m 4 m 5 m 2 cm 5 cm 14 cm 11 What is th ara of a rctangl with a primtr of 32 cm and a lngth of 10 cm? 12 What is th primtr of a squar with an ara of 25 cm 2? 13 Blow is a map of th availabl floor spac (shadd) in an unoccupid car show-room. Calculat th ara availabl for a display m 4 m 10 m 22 m 1 Copy and complt th following magic squars. (b) MATHS ZONE 7

46 2 Round ths numbrs off to th first digit. 29 (b) 7390 (c) 5 3 Arrang th following sts of numbrs in ordr from smallst to largst. 0, 8, 10, 15, 2 (b) 102, 56, 156, 110, 78 (c) 63, 38, 78, 21, 0 4 Evaluat th following: 3 + (9 7) ( 2) (b) 5 ( 4) ( 1 + 3) (c) 24 ( ) ( 1) 5 Which of ths numbrs ar divisibl by 6? 2356, 876, 444, 6783, , List all th factors of th following numbrs. 25 (b) 101 (c) 42 (d) 70 7 Copy ths pattrns and fill in th missing numbrs. 10, 6, 2,,, (b) 1,, 9, 16,, 8 Look at th following tabls and us th pronumrals givn in ach cas to writ th rul out as a formula. x y (b) a b (c) m n Draw angls of th following sizs. 270 (b) 32 (c) 108 (d) Which on of th following is a pair of supplmntary angls? A 0 and 90 B 40 and 140 C 50 and 150 D 300 and Calculat: (b) (c) Calculat: (b) (c) , 6.11 Assignmnt 7 7 lngth, primtr and AREA 273