H SERIES. Area and Perimeter. Curriculum Ready ACMMG: 109, 159, 196,

Transcription

1 Are n Perimeter Curriulum Rey ACMMG: 0, 5, 6, 6

2 Copyright 00 3P Lerning. All rights reserve. First eition printe 00 in Austrli. A tlogue reor for this ook is ville from 3P Lerning Lt. ISBN Ownership of ontent The mterils in this resoure, inluing without limittion ll informtion, text, grphis, vertisements, nmes, logos n tre mrks (Content) re protete y opyright, tre mrk n other intelletul property lws unless expressly inite otherwise. You must not moify, opy, reproue, repulish or istriute this Content in ny wy exept s expressly provie for in these Generl Conitions or with our express prior written onsent. Copyright Copyright in this resoure is owne or liense y us. Other thn for the purposes of, n sujet to the onitions presrie uner, the Copyright At 68 (Cth) n similr legisltion whih pplies in your lotion, n exept s expressly uthorise y these Generl Conitions, you my not in ny form or y ny mens: pt, reproue, store, istriute, print, isply, perform, pulish or rete erivtive works from ny prt of this resoure; or ommerilise ny informtion, prouts or servies otine from ny prt of this resoure. Where opyright legisltion in lotion inlues remunerte sheme to permit eutionl institutions to opy or print ny prt of the resoure, we will lim for remunertion uner tht sheme where worksheets re printe or photoopie y tehers for use y stuents, n where tehers iret stuents to print or photoopy worksheets for use y stuents t shool. A worksheet is pge of lerning, esigne for stuent to write on using n ink pen or penil. This my le to n inrese in the fees for eutionl institutions to prtiipte in the relevnt sheme. Pulishe 3P Lerning Lt For more opies of this ook, ontt us t: Designe 3P Lerning Lt Although every preution hs een tken in the preprtion of this ook, the pulisher n uthors ssume no responsiility for errors or omissions. Neither is ny liility ssume for mges resulting from the use of this informtion ontine herein.

3 This ooklet shows how to lulte the re n perimeter of ommon plne shpes. Footll fiels use retngles, irles, qurnts n minor segments with speifi res n perimeters to mrk out the plying fiel. Write own the nme of nother sport tht uses plying fiel or ourt n list ll the plne shpes use to rete them elow (inlue smll sketh to help you out): Sport: Shpes list: Q Use ll four squres elow to mke two shpes in whih the numer of sies is lso equl to four. Compre the istne roun the outsie of your two shpes. Write own wht you isovere n whether or not it ws ifferent from wht you expete. Work through the ook for gret wy to o this Mthletis 3P Lerning Lt

4 ow oes it work? Are using unit squres Are is the mount of flt spe shpe hs insie its eges or ounries. A unit squre is squre with eh sie extly one unit of mesurement long. unit Little shes on eh sie men they re ll the sme length. Are (A) squre unit unit (in shorter, units form) So the re of the she shpe elow is foun y simply ounting the numer of unit squres tht mke it. unit 3 4 Are (A) 0 squre units unit ere re some exmples inluing hlves n qurters of unit squres: Clulte the re of these shpes (i) unit Are ( A) whole squre units + hlf squre units squre units+ # squre units ^+ h squre units 3 units When single units of mesurement re given, they re use inste of the wor units. (ii) m Are ( A) whole squres+ hlf squres + qurter squres squre m + # squrem + # 4 squre m ^ h squre entimetres 35. m Mthletis 3P Lerning Lt

5 ow oes it work? Your Turn Are using unit squres Clulte the re of ll these she shpes: unit mm Are whole squres Are whole squres units mm unit m Are whole + hlf squres Are whole + hlf squres m + # m units + # units m units e f unit Are whole + qurter squres m Are whole + qurter squres units + # units 4 m + # m 4 units m g Are whole + hlf + qurter squres unit units + # units + # units 4 units Mthletis 3P Lerning Lt 3

6 ow oes it work? Your Turn Are using unit squres Clulte the re of these she shpes, using the orret short version for the units: m unit Are Are mm m Are Are e f mm unit Are Are g km h AREAUSINGUNITSQUARES *AREAUSINGUNITSQUARES *.../.../ 0... m Are Are 4 Mthletis 3P Lerning Lt

7 ow oes it work? Your Turn Are using unit squres 3 She shpes on these squre gris to mth the re written in squre rkets. 68 using whole squres only. 65 inlue hlf squres in your shpe. unit unit 63 inlue qurter squres in your shpe inlue hlves n qurters. mm m 4 An rtist hs eight, m, squre-shpe pnels whih he n use to mke pttern. The rules for the esign re: - the shpe forme nnot hve ny gps/holes. i.e. or m - it must fit entirely insie the isply pnel shown, - ll the eight pnels must e use in eh esign. ow mny ifferent esigns n you ome up with? Sketh the min shpes to help you rememer your ount. Numer of ifferent esigns you foun Mthletis 3P Lerning Lt 5

8 ow oes it work? Perimeter using unit squres The wor perimeter is omintion of two Greek wors peri (roun) n meter (mesure). Fining the perimeter (P) mens mesuring the istne roun the outsie! Strt/en of pth roun the outsie unit Perimeter( P) unit+ unit+ unit+ unit 4 # unit 4 units Rememer, little shes on eh sie men they re ll the sme length. These exmples shows tht we only ount ll the outsie eges. Clulte the perimeter of these shpes forme using unit shpes (i) units Strt/en of pth roun the outsie unit unit units Perimeter( P) units 6 units Sies of unit squres insie the shpe not inlue It oes not mtter where you strt/finish, ut it is usully esiest to strt from one orner. (ii) 3 units unit unit unit unit unit unit unit unit Strt/en of pth roun the outsie Perimeter( P) units units 6 Mthletis 3P Lerning Lt

9 ow oes it work? Your Turn Perimeter using unit squres PERIMETERUSINGUNITSQUARES *PERIMETERUSINGUNITSQUARES * Clulte the perimeter of these she shpes: unit Perimeter units.../.../ 0... units Perimeter units unit units Perimeter units unit units Write the length of the perimeter (P) for eh of these she shpes: P units P units P units P units 3 The she shpes in ll hve the sme re of 6 units. Use your results in question to help you explin riefly whether or not ll shpes with the sme re hve the sme perimeter. Mthletis 3P Lerning Lt 7

10 ow oes it work? Your Turn Perimeter using unit squres 4 Drw six ptterns on the gri elow whih: ll hve n re of 5 units n, hve ifferent perimeter from eh other. All squres use for eh pttern must shre t lest one ommon sie or orner point. unit Drw nother five ptterns on the gri elow whih: ll hve n re of 5 units n, hve ifferent perimeter thn the shpes forme in prt. All squres use for eh pttern must shre t lest hlf of ommon sie point. unit or orner unit unit 8 Mthletis 3P Lerning Lt

11 Where oes it work? Are: Squres n retngles A simple multiplition will let you lulte the re of squres n retngles. For squres n retngles, just multiply the length of the perpeniulr sies (Length n with). Length Length With Squre Sie (x) With Retngle Sie (y) Sie (x) Are length # with Sie ^xhunits # Sie^xhunits x x # x units units Sie (x) Are length # with Sie ^xhunits # Sie^yhunits x # xy y units units ere re some exmples involving numeril lengths: Clulte the re of these she shpes (i) 4 units Are length # with 4units # 4units 4 units 6 units So why units squre for re? 4units # 4units 4 # 4units # units 4 # units 6 units (ii) Are length # with.5 mm 6mm #.5 mm mm Units of re mth units of sie length 6 mm All mesurements (or imensions) must e written in the sme units efore lulting the re. (iii) Are length # with 60 m m # 60 m 00m # 60 m Write oth lengths using the sme unit m 000 m Units of re mth units of sie length Mthletis 3P Lerning Lt

12 * AREA: SQUARES* AREA: SQUARES AND RECTANGLES Where oes it work? Your Turn Are: Squres n retngles Clulte the re of these squres n retngles, nswering using the pproprite units. Are # units Are # m length with length with units units 0.6 m m Are # units Are # mm 3 units length with 5 mm length with units units 3. mm mm Clulte the re of these squres n retngles. Roun your nswers to nerest whole squre unit..4 km 7 m 43 mm AND RECTANGLES.../.../ 0... Are # km Are # m length with length with km m. km (to nerest whole km ). m (to nerest whole m ) 3 Wht is the length of this retngle? Are 8 units 4 units 4 Wht re the imensions of squre with n re of m? Psst: rememer the opposite of squring numers is lulting the squre root. 0 Mthletis 3P Lerning Lt

13 Where oes it work? Are: Tringles Look t this tringle rwn insie retngle. eight (Length) Bse (with) The tringle is extly hlf the size of the retngle ` Are of the tringle hlf the re of the retngle units of with (se () for tringle) # Length (height (h) for tringle) units # # h units This rule works to fin the re for ll tringles! ere re some exmples involving numeril imensions: Clulte the re of the she tringles elow (i) 4 m 5 m Are # se # height # 3m # 4m eight use the perpeniulr height 6 m 6 m The rule lso works for this next tringle whih is just the hlves of two retngles omine. (ii) Are # se # height ere, we sy the height is the perpeniulr 4 mm # 54. mm # 4mm istne of the thir vertex from the se mm 5.4 mm For unusul tringles like this she one, we still multiply the se n the perpeniulr height n hlve it. (iii) Are # se # height units # 5. units # units 5. units.5 units Mthletis 3P Lerning Lt

14 Where oes it work? Your Turn Are: Tringles *AREA:TRIANGLES *AREA:TRIANGLES *AREA:TRIANGLES Clulte the re of the tringle tht uts these two shpes in hlf..../.../ units 8 units units Are # # units Are # # units se height se height units units Clulte the re of these she tringles: 4 m 8 mm m mm Are # # mm Are # # m mm m 0 units 7.5 units 4.5 m 600 m Rememer: sme units neee. Are # # units Are # # m units m e Are # # m 4 m 5 m m Mthletis 3P Lerning Lt

15 Where oes it work? Are: Prllelogrms Prllelogrms hve opposite sies equl in length n prllel (lwys the sme istne prt). Perpeniulr height (h) The shortest istne etween pir of prllel sies is lle the perpeniulr height We n mke them look like retngle y utting the tringle off one en n moving it to the other. height Prllelogrm move tringle ut off Retngle ` Are of prllelogrm Are of the retngle forme fter moving tringle length # perpeniulr height units l # h units Clulte the re of these prllelogrms (i) Are length # height 0 mm 5 mm 30 mm # 5 mm 30 mm 450 mm A prllelogrm n lso e forme joining together two ientil tringles. (ii) Fin the re of the prllelogrm forme using two of these right ngle tringles: 5 m 5 m 3 m 5 m m 3 m m m 3 m 3 m m 3 m m 5 m Copy n flip oth vertilly n horizontlly 5 m Bring them together 5 m Prllelogrm Are # re of the tringle Are length # perpeniulr height # # 5m # m OR 5m # m 60 m 60 m Mthletis 3P Lerning Lt 3

16 Where oes it work? Your Turn Are: Prllelogrms Complete the re lultions for these prllelogrms: AREA: PARALLELOGRAM.../.../ 0... ** AREA:PARALLELOGRAM 0 units. m 3. m 4.5 mm 4.6 m Are # units Are # m length height length height units m Clulte the re of the prllelogrms forme using these tringles. 6 m 0 m mm.6 mm 4 m. mm Are m Are mm 3 Fill the gri elow with s mny ifferent prllelogrms s you n whih hve n re of 4 units. unit unit 4 Mthletis 3P Lerning Lt

17 Where oes it work? Are of omposite shpes When ommon shpes re put together, the new shpe me is lle omposite shpe. Common shpe (Retngle) + Common shpe (Isoseles tringle) Just lulte the re of eh shpe seprtely then (or sutrt) to fin the totl omposite re. Clulte the re of these omposite shpes Composite shpe (Retngle + Isoseles tringle) Composite just mens it is me y putting together seprte prts (i) Split into tringle n squre. 8 m Are # m # 8 m 8 m 0 m Are 8 m # 8 m 64 m 8 m ` Totl re Are + Are 8 m + 64 m A re n for the omposite re m 8 m 7 m This next one shows how you n use ition or sutrtion to lulte the re of omposite shpes. (ii) 3.5 m metho : Split into two retngles n 8 m 7 m 3.5 m 4.5 m Are 4.5 m # 3.5 m 5.75 m Are 3.5 m # 7 m 4.5 m ` Totl re 5.75 m m A re n re together 40.5 m 3.5 m 7 m metho : Lrge retngle minus the smll 'ut out' retngle 3.5 m Are 8 m # 7 m 56 m 8 m 4.5 m Are 3.5 m # 4.5 m 5.75 m 7 m ` Totl re 56 m m 40.5 m Sutrt re from re Mthletis 3P Lerning Lt 5

18 Where oes it work? Your Turn Are of omposite shpes Complete the re lultions for these she shpes: 6 mm 4 mm Are mm # mm Are mm # mm mm mm 4 mm mm ` Composite re + mm mm m 6 m 6 m 3 m 3 m m 5 m 5 m Are # # m Are # m m m ` Composite re + m m 6.5 m m Are # m Are # # m.5 m m m 6.5 m m ` Composite re - m 4 m.5 m m 5 m Are # # m Are # m 3 m m m m ` Composite re - m 5 m m 3 m m 6 Mthletis 3P Lerning Lt

19 AREA OF COMPOSITEAREA OF COMPOSITE SAPES * Where oes it work? Your Turn Are of omposite shpes Clulte the re of these omposite shpes, showing ll working: SAPES *.../.../ m 5 m m Are m psst: hnge ll the units to metres first. 300 m 00 m Are m 4.5 m mm Are mm psst: this one nees three re lultions 6 units 0 units 5 units Are units Mthletis 3P Lerning Lt 7

20 Where oes it work? Perimeter of simple shpes By ing together the lengths of eh sie, the perimeter of ll ommon shpes n e foun. Strt/finish Strt/finish Squre with (y units) Retngle sie (y units) Tringle sie 3 (z units) sie (x units) length (x units) P 4 # sie length P with+ length+ with + length 4 # x units ^y+ x+ y+ xh units 4x units ^ # xh+ ^ # yhunits x+ yunits ere re some exmples involving numeril imensions: sie (x units) Strt/finish P sie + sie + sie 3 x+ y+ z units You n strt/en t ny vertex of the shpe Clulte the perimeter of these ommon shpes (i) units 8 units units 8 units Sum of ll the sie lengths 0 units Strt/finish 0 units Perimeter units + 8units+ 0 units units (ii) Strt/finish.3 m.3 m.3 m Four lots of the sme sie length.3 m.3 m Perimeter 4 # 3. m. m All mesurements must e in the sme units efore lulting perimeter. (iii) The perimeter for prllelogrms is one the sme s for retngles. Clulte this perimeter in mm. 5 mm 5 mm Strt/finish 0.5 m 5 mm 5 mm All sie lengths in mm 5 mm Perimeter # 5mm+ # 5 mm 30 mm + 0 mm 40 mm Opposite sies in pirs 8 Mthletis 3P Lerning Lt

21 Where oes it work? Your Turn Perimeter of simple shpes Complete the perimeter lultions for these shpes: OF SIMPLE SAPES * PERIMETER OF SIMPLE SAPES * PERIMETER..... /..... / units Perimeter units + units + units 5 units 8 units units mm Perimeter # mm + # mm mm 6 mm Perimeter # m m 5 m Perimeter # m + m m m 5 m Clulte the perimeter of the shpes elow, using the spe to show ll working: 5 m 5.8 m Perimeter m Perimeter m.6 mm 3 m 5 m 3.4 m.4 mm.6 m.4 m Perimeter mm Perimeter m Mthletis 3P Lerning Lt

22 Where oes it work? Your Turn Perimeter of simple shpes 3 Fin the perimeter of eh shpe written using the smller units of mesurement in eh igrm. in m. in mm. 550 m 3 m 600 m 6.5 m 5 mm Perimeter m Perimeter mm 4 Eh shpe elow hs its perimeter written insie n is missing one of the sie length vlues. Rule stright line etween eh shpe n the orret missing sie length on the right to nswer: ow mny stright sies oes n iosgon hve? 4.4 m P 4 m 5. m P m F E V L N T 8 m.4 m 3.5 m 380 m P 3 m m W S v 440 m m P 4 m 6.5 m P 8 m m N v E Y T R G 7 m 650 m. m 6 m.6 m P m 5 m m v 0 Mthletis 3P Lerning Lt

23 Where oes it work? Perimeter of omposite shpes The lengths of the unlelle sies must e foun in omposite shpes efore lulting their perimeter.? m ( ) m 6.5 m m m 7 m 3.5 m 7 m 3.5 m? m (7 - ) m 5 m Strt/finish 3 m 3 m ` Perimeter 7m+ 6.5 m+ m+ 3.5m+ 5m+ 3m 7 m ere re some more exmples. Clulte the perimeter of these omposite shpes (i) m m 30 mm m 5 m m 3 m Clulte eh sie length of the shpe in the sme units m + 5 m 4 m ` Perimeter m+ 3m+ 4m+ m 48 m (ii) 3 m You n lso imgine the sies re-positione to mke the lultion esier 6 m ^6m- 3 mh'.5 m 3 m 3 m.5 m +.5 m 3 m 6 m 6 m ` # Perimeter 6.5 m+ 3m+ 6m 8 m ` Perimeter # 6m+ # 3m 8 m Mthletis 3P Lerning Lt

24 Where oes it work? Your Turn Perimeter of omposite shpes Clulte the vlue of the sies lelle n in eh of these omposite shpes: 3 m m 8 m m m. mm mm 3.4 mm.6 mm mm mm 8 m 5 m m m 4 m 5 m 4.8 m 8 m m m 5 m Clulte the perimeter of these omposite shpes: Perimeter # m.8 mm m PERIMETER OF COMPOSITE SAPES * PERIMETER OF COMPOSITE SAPES * m Perimeter # m + # m 3.../.../ 0... m 4 m m + m Be reful with the units for these next two m. m 6 mm 0 mm Perimeter 3 # mm + mm + mm mm 4. m 38 mm Perimeter # 4. m + # m m Mthletis Pssport 3P Lerning

25 Where oes it work? Your Turn Perimeter of omposite shpes 3 Clulte the perimeter of these omposite shpes in the units given in squre rkets. Show ll working. 6 mm@ 6 m@ 4 mm. m Perimeter mm Perimeter m 6 m@ 48 mm 6 km@ psst: km m.5 km 3.6 m mm 00 m Perimeter m Perimeter km 4 Ern n wesome pssport stmp for this one! The inomplete geometri pth shown elow is eing onstrute using omintion of the following shpe pvers: m m m m m.4 m.4 m m The gp in etween eh prt of the spirl pth is lwys m wie. Clulte wht the totl perimeter of this pth will e when finishe. Complete pth m m AWESOMEAWESOME AWESOMEAWESOME AWESOME AWESOME.../.../ 0... Totl perimeter of omplete pth m Mthletis Pssport 3P Lerning 3

26 Where oes it work? Your Turn Perimeter of omposite shpes 5 The four omposite shpes elow hve een forme using five, unit squres. Using your knowlege of perimeter n the gri elow, omine ll four piees to rete two ifferent shpes so tht: One shpe hs the smllest possile perimeter. The other hs the lrgest possile perimeter. All shpes must e onnete y t lest one whole sie of unit squre. unit unit Briefly esrie the strtegy you use to hieve eh outome elow: A shpe with the smllest possile perimeter. A shpe with the lrgest possile perimeter. 4 Mthletis 3P Lerning Lt

27 Where oes it work? Simple wor prolems involving re n perimeter Sometimes we n only ommunite ies or prolems through wors. So it is importnt to e le to tke written/spoken informtion n turn it into something useful. For exmple, Miguel wnts to pint squre. e hs just enough pint to rete line 40 m long. Wht is the longest length eh sie of the squre n e if he wishes to use ll of the pint? To use up ll the pint, the totl perimeter of the squre must equl 40 m. So eh sie length 40m ' 4 60 m ` The longest length eh sie of the squre pinte y Miguel n e is 60 m. This is useful for Miguel to know euse if he pinte the first sie too long, he woul run out of pint! ere re some more exmples (i) A retngulr prk is four times longer thn it is wie. If the prk is 0 m long, how muh re oes this prk over? ^0 ' 4hm.5 m Drw igrm to illustrte prolem (ii) 0 m Are length # with 0 m #.5 m 05 m At fun run, ompetitors run stright for 0. km efore turning left 0 egrees to run stright for further. km. The ourse hs one finl orner whih les k to the strt long stright.5 km long street. ow mny lps of this ourse o ompetitors omplete if they run totl of 8 km?. km.5 km 0. km Drw igrm to illustrte prolem Strt/finish Perimeter ofourse 0.km+. km+.5 km 3.6 km Perimeter will e the length of eh lp ` Length of eh lp of the ourse is 3.6 km ` Numer of lps 8 km' 36. km Re istne ivie y the length of eh lp 5 ` Competitors must omplete 5 lps of the ourse to finish Mthletis 3P Lerning Lt 5

28 Where oes it work? Your Turn Simple wor prolems involving re n perimeter Three equilterl tringles, eh with sies of length 3 m hve een ple together to mke one lose four-sie shpe. Eh tringle shres t lest one whole sie with nother. Clulte the perimeter of the shpe forme. Use ll four squres elow to mke two shpes in whih the numer of sies is lso equl to four. Compre the istne roun the outsie of your two shpes n explin wht this shows us out the reltionship etween re n perimeter. You hve een employe y fri esign ompny lle Doule Geometris. Your first tsk s pttern mker is to esign the following using ll seven ientil squres: Close shpes for new pttern in whih the vlue of their perimeter is twie the vlue of their re. Drw five possile ifferent ptterns tht mth this esign request. 3 The se length of right-ngle tringle is one fifth of its height. If the se of this tringle is 4. m, lulte the re of the tringle. SIMPLE WORD PROBLEMS INVOLVING AREA AND PERIMETER.../.../ Mthletis 3P Lerning Lt

29 Where oes it work? Your Turn Simple wor prolems involving re n perimeter 4 An rhitet is ske to esign n rt gllery uiling. One of the esign rules is tht the floor must e retngle shpe with n re of 64 m. If only whole metre mesurements n e use, sketh ll the ifferent possile floor imensions. Another esign rule is to try ensure lrge perimeter so there is more spe to hng pintings from. Use lultions to show whih floor pln will hve the lrgest perimeter. Woul the esign with the lrgest possile perimeter e goo hoie? Explin riefly why/why not. A smll rt piee t the gllery hs one sie of n envelope ompletely overe in stmps like the one piture elow. ow mny of these stmps were neee to over one sie of n envelope.5 m wie n 4.5 m long if they ll fit perfetly without ny eges overlpping?.5 m 3.5 m.5 m 4.5 m Mthletis 3P Lerning Lt 7

30 Where oes it work? Your Turn Simple wor prolems involving re n perimeter 5 A fene use to lose off prllelogrm-shpe re is eing rerrnge to rete squre re with the sme perimeter. The short sie of the re is 34 m long (hlf the length of the long sie). ow long will eh sie of the new squre re e fter using the whole length of this fene? 34 m 6 If the istne etween the longer sies of the originl re ws 30 m n the length i not hnge, use lultions to show whih fening rrngement surroune the lrgest re. A wll is rete y stking equl-size retngulr riks on top of eh other s shown. The en of eh retngle sits extly hlf-wy long the long sie of the retngle unerneth it. Eh rik 6 m 8 m 8 A 500 ml tin of white pint hs een purhse to pint the wll. The instrutions on the pint tin sy this is enough to over n re of 500 m. Use lultions to show tht there is enough pint in the tin to over sie of the wll. If eetle wlke ll roun the outsie of the wll (inluing long the groun), how mny metres i it wlk? Mthletis Pssport 3P Lerning

31 Wht else n you o? Rhomus n Kite shpes The re for oth of these shpes n e lulte the sme wy using the length of their igonls. A B A Rhomus is A rhomus is like squre prllelogrm. prllelogrm, so Are ^igonl lengths multiplietogetherh ' we n lso use the sme rule to D C ^AC # BDh ' fin the re: A B C Perimeter 4 # 4 # AB lengthofone sie length A kite hs two pirs of equl sies whih re jent (next to) eh other. Are ^igonl lengths multiplietogetherh ' height ^AC # BDh ' Perimeter # short sie + # long sie D AB + ere re some exmples: Clulte the re n perimeter of these shpes # # AD (i) For this rhomus, WY m n XZ 6 m. W X Are ^igonl lengths multiplietogetherh ' ^ m # 6 mh ' Z 0 m Y Perimeter 6 m 4 # lengthofsies 4 # 0 m 40 m (ii) For the kite ABCD shown elow, AC 4.7 m n BD. m. A.5 m B 3.7 m Are ^igonl lengths multiplietogetherh ' ^. m # 47. mh ' 435. m D C Perimeter # short sie + # long sie # 5. m+ # 3.7 m 0.4 m Mthletis 3P Lerning Lt

32 Wht else n you o? Your Turn Rhomus n Kite shpes Clulte the re n perimeter of these shpes: PR 8 m n QS 5 m Q BD.8 mm n AC.4 mm.../.../ 0... RROMBUS AND KITE SAPES OMBUS AND KITE SAPES 4 m A B P S R 5 m D 3.6 mm C Are # ' m m Are # # mm mm ' # Perimeter # + # m Perimeter # mm m mm Clulte the perimeter of these omposite shpes: 4 m 6.5 m 3.4 m m 5. m Perimeter m Perimeter m 3 Clulte the re of this omposite shpe, showing ll working when: J L 30 m, IK IM 6 m n JL m I K M L Are m 30 Mthletis 3P Lerning Lt

33 Wht else n you o? Trpeziums A trpezium is qurilterl whih hs t lest one pir of prllel sies. Squres, retngles, prllelogrms n rhomi re ll just speil types of trpeziums. So the re formul for trpezium woul lso work on ll of those shpes. A B A B height (h) height (h) C D C D Two ommon trpezium shpes ere re some exmples: In oth shpes, the sies AB () n CD () re prllel ( AB CD ). The height is the perpeniulr istne etween the prllel sies. : Are ^sumofthe prllelsiesh # height ' ^+ h # h ' : Perimeter AB + BD + CD + AC Clulte the re n perimeter of these shpes (i) 0 mm Are ^sumof the prllelsiesh # height ' ^ mm + 0 mmh # 6 mm ' 3 mm # 6 mm ' 0 mm mm 56 mm Perimeter 0 mm+ mm+ 6 mm+ 0 mm 6 mm 68 mm (ii) 6.7 m Are ^sumof the prllelsiesh # height '. m m 0. m ^67. m+ 4. 5mh # m ' 4.5 m. m # m'. m Perimeter 67. m+ 0. m+ 45. m+. m 34. m Mthletis 3P Lerning Lt 3

34 Wht else n you o? Your Turn TRAPEZIUMS * TRAPEZIUMS * TRAPEZIUMS * TRAPEZIUMS * Trpeziums Clulte the re n perimeter of these trpeziums: km.5 m.../.../ km km 4 km.8 m 8. m 53 km 4.5 m Are + # ' km Are + # ' m km m Perimeter km Perimeter m Use the trpezium metho to lulte the re of these omposite plne shpes. 8 m 5 m mm.4 mm 4.3 mm 5 m Are m Are mm 3 Use the trpezium metho to lulte the re of this omposite plne shpes m 70 m 6.7 m 40 m Are m Perimeter m 3 Mthletis 3P Lerning Lt

35 Wht else n you o? Your Turn Are hllenge Fill the gri elow with s mny ifferent squres, tringles, retngles, prllelogrms, rhomi, kites n trpeziums s you n whih ll hve the sme re of 8 units. unit unit Mthletis 3P Lerning Lt 33

36 Wht else n you o? Your Turn Refletion Time Refleting on the work overe within this ooklet: Wht useful skills hve you gine y lerning how to lulte the re n perimeter of plne shpes? Write out one or two wys you think you oul pply re n perimeter lultions to rel life sitution. If you isovere or lernt out ny shortuts to help with lulting re n perimeter or some other ool fts/onversions, jot them own here: 34 Mthletis 3P Lerning Lt

37 Chet Sheet ere is wht you nee to rememer from this topi on Are n perimeter Are using unit squres Are is just the mount of flt spe shpe hs insie its eges or ounries. A unit squre is squre with eh sie extly one unit of mesurement long. Count the totl numer of whole squres, or frtions of squres to lulte the re. Are (A) units Perimeter using unit squres The perimeter with unit squres mens ount the numer of eges roun the outsie of the shpe. Perimeter (P) 6 units Are: Squres n retngles Just multiply the length of the perpeniulr sies (length n with). length length with Squre sie (x) with Retngle sie (y) sie (x) Are length # with x units sie (x) Are length # with xy units Are: Tringles height height height Are: Prllelogrms se se se ` Are of the tringle (hlf the se multiplie y the perpeniulr height) units # # h units Perpeniulr height (h) Length (l) ` Are of prllelogrm length # perpeniulr height units l # h units Mthletis 3P Lerning Lt 35

38 Chet Sheet Are of omposite shpes + Are (Retngle) + Are (Isoseles tringle) Composite Are Are + Are (Retngle + Isoseles tringle) Perimeter of simple shpes A together the lengths of every sie whih mke the shpe. Strt/finish Strt/finish Squre with (y units) Retngle sie (y units) Tringle sie 3 (z units) P 4 sie (x units) # 4x units sie length length (x units) P with+ length+ with + length x+ yunits sie (x units) Strt/finish P sie + sie + sie 3 x+ y+ z units Perimeter of omposite shpes The lengths of ll unlelle sies must e foun in omposite shpes efore lulting their perimeter. It is esier to them together if the lengths re ll in the sme units.? m ( ) m 6.5 m m m 7 m 3.5 m 7 m 3.5 m? m (7 - ) m 5 m Strt/finish 3 m 3 m ` Perimeter 7m+ 6.5 m+ m+ 3.5m+ 5m+ 3m 7 m Rhomus, Kites n Trpeziums B A B A C A D C C D Rhomus Kite Are ^AC # BDh' Are ( AC # BD) ' Perimeter 4 # AB Perimeter # AB + # AD B perpeniulr height (h) D A C Are ( + ) # h ' Perimeter AB + BD + CD + AC perpeniulr height (h) Trpezium B D 36 Mthletis 3P Lerning Lt

39 Answers Are using unit squres Are using unit squres. Are 4 whole squres 4 units 4. ere re 4 solutions. There re more... Are 6 whole squres 6 mm Are whole + hlf squres m + # m 3 m Are 4 whole + 4 hlf squres 4 units + 4 # units 6 units e Are whole + 4 qurter squres units + 4 # units 4 3 units f Are 4 whole + qurter squres 4 m + # m m g Are 3 whole + 4 hlf + 4 qurter squres 3 units + 4 # units + 4 # units 4 6 units. Are m Are 4.5 mm Are units e g Are 6 m f Are 8 mm Are 5 units Are.5 km h Are 4 m. Perimeter using unit squres Perimeter units 8 units 3. Perimeter units 8 units Perimeter units 8 units. P 0 units P units P 4 units P 3 units 3. Even though the shpes ll hve the sme re, they o not ll hve the sme perimeter lengths. This shows tht the shpes with the sme re will not neessrily hve the sme perimeter. So the perimeter is not relte to the re of the shpe. Mthletis 3P Lerning Lt 37

40 Answers Perimeter using unit squres Are: Tringles 4.. Are # # 4 units 4 units Are # 8 # 8 units P 0 units P units P 4 units 3 units. Are # # 8 mm 48 mm P 6 units P 8 units P 0 units Are # 4 # m 84 m Are # 0 # 7.5 units P units P 3 units P 5 units 37.5 units Are # 6 # 4.5 m 3.5 m P 7 units P units e Are # 5 # 4 m 0 m. Are: Squres n retngles Are: Prllelogrms Are # units Are 0.6 # 0.6 m. 4 units Are 4.5 # 0 units Are 4.6 #. m 0.36 m 450 units 0. m Are 3 # units Are 5 # 3. mm 6 units 6 mm. Are 40 m Are. mm. Are.4 #.4 km.6 km. km (to nerest whole km ) 3. Are 7 # 4.3 m 30. m. 30 m (to nerest whole m ) 3. The length of the retngle is 7 units. 4. The length of eh sie is units 38 Mthletis 3P Lerning Lt

41 Answers Are of omposite shpes. Are 4 mm # 4 mm 6 mm. Are mm # mm 4 mm 3. Composite re mm 0 mm 4. Are 0.5 # 6 # 8 m 4 m Are # 5 m 55 m Composite re m. 7 m Are 6.5 # m 3 m Are 0.5 # 4 # m 4 m. Composite re 3-4 m m Are 0.5 # 8 # 5 m 0 m Are # m 4 m Composite re 0-4 m 6 m Perimeter of simple shpes Perimeter of omposite shpes Perimeter 3. m Perimeter 8 mm Perimeter 450 m T W E N T Y m v 4 m 5 m m 6 m Perimeter 5 #.8 m 4 m Perimeter # m + # m m + 4 m 6 m Perimeter 45 m Perimeter 0.8 m Perimeter 780 mm.8 mm. mm 5. m. m Perimeter 3 # mm + 0 mm + 6 mm 7 mm Perimeter 4 # 4. m + # 3.8 m 4 m. Are m Are 3 mm Are.5 m Are 0 units 3. Perimeter 48 mm Perimeter. m Perimeter 6.4 m Perimeter 6.6 km Perimeter of simple shpes 4. Totl perimeter of omplete pth 3 m. Perimeter 5 units + 7 units + 8 units 40 units Perimeter # mm + # 6 mm 30 mm Perimeter 4 # 5 m 0 m Perimeter # m + 5 m 7 m Mthletis 3P Lerning Lt 3

42 Answers 5. Perimeter of omposite shpes. Simple wor prolems involving re n perimeter Smllest possile perimeter 8 units 3. Are of tringle 44. m Lrgest possile perimeter 40 units 4. Try to mke s mny sies s possile touhing eh other, whih reues the numer of sies tht re ounte for the perimeter. 64 m m 3 m 4 m Mking eh shpe joine to the other y one sie only, whih inreses the numer of sies tht must ounte for the perimeter. 4 3 m 8 m 6 m. Simple wor prolems involving re n perimeter Perimeter 5 m 8 m 3 Perimeter 30 m Perimeter 68 m Perimeter 40 m Perimeter 3 m Floor pln hs the lrgest perimeter 4. Shpe Perimeter 0 units No, floor pln woul not e goo hoie. While it meets the rule of hving the lrgest possile perimeter, it woul e very long n too nrrow for more thn one person to wlk through t time. Shpe Totl numer of stmps tht fit 35 stmps Perimeter 8 units 5. Eh sie of the new squre re 5 m long The re of oth shpes is the sme, ut the perimeters re ifferent. This shows tht there is no reltionship etween the re n the perimeter of shpe. 6. The new squre shpe will surroun more re. There will e just enough pint to over the sie of the wll (with 300 m to spre) The eetle wlke totl istne of 5.5 m 40 Mthletis 3P Lerning Lt

43 Answers Rhomus n Kite shpes Trpeziums. Are 8 # 5 ' m. 468 m Are.8 #.4 # mm.6 mm Perimeter # 4 + # 5 m m Are (53 + ) # ' km 43 km Perimeter 0 km Are ( ) #.8 ' m 5.3 m Perimeter 7 m Perimeter 4 # 3.6 mm 4.4 mm. Are 35 m Are 4. mm. Perimeter 64 m Perimeter 3.7 m 3. Are m Perimeter 74 m 3. Are 408 m Are hllenge ere re 0 possile shpes whih ll hve n re of 8 units. There re mny more. Mthletis 3P Lerning Lt 4

44 Notes 4 Mthletis 3P Lerning Lt

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