Area and Perimeter. Area and Perimeter. Curriculum Ready.

Transcription

1 Are nd Perimeter Curriculum Redy

2

3 This ooklet shows how to clculte the re nd perimeter of common plne shpes. Footll fields use rectngles, circles, qudrnts nd minor segments with specific res nd perimeters to mrk out the plying field. Write down the nme of nother sport tht uses plying field or court nd list ll the plne shpes used to crete them elow (include smll sketch to help you out): Sport: Shpes list: Q Use ll four squres elow to mke two shpes in which the numer of sides is lso equl to four. Compre the distnce round the outside of your two shpes. Write down wht you discovered nd whether or not it ws different from wht you expected. Work through the ook for gret wy to do this Mthletics Pssport 3P Lerning 9

4 ow does it work? Are using unit squres Are is just the mount of flt spce shpe hs inside its edges or oundries. A unit squre is squre with ech side exctly one unit of mesurement long. Little dshes on ech side men they re ll the sme length. Are (A) = squre unit = (in shorter, units form) So the re of the shded shpe elow is found y simply counting the numer of unit squres tht mke it. 3 4 Are (A) = 0 squre units 5 6 = 0 unit ere re some exmples including hlves nd qurters of unit squres: Clculte the re of these shpes (i) 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 used insted of the word units. (ii) Are ( A) = whole squres + hlf squres+ qurter squres = squre cm + # squre cm + # squre cm 4 = ^ h squre centimetres cm = 35. cm 9 Mthletics Pssport 3P Lerning

5 ow does it work? Are using unit squres Clculte the re of ll these shded shpes: mm Are = whole squres Are = whole squres = units = mm c d m Are = whole + hlf squres Are = whole + hlf squres = m + # m = units + # units = m = units e f cm Are = whole + qurter squres Are = whole + qurter squres = units + # units 4 = cm + # cm 4 = units = cm g Are = whole + hlf + qurter squres = units + # units + # units 4 = units Mthletics Pssport 3P Lerning 9 3

6 ow does it work? Are using unit squres Clculte the re of these shded shpes, using the correct short version for the units: cm Are = Are = c d mm m Are = Are = e f mm Are = Are = g km h AREAUSINGUNITSQUARES *AREAUSINGUNITSQUARES *.../.../ 0... cm Are = Are = 4 9 Mthletics Pssport 3P Lerning

7 ow does it work? Are using unit squres 3 Shde shpes on these squre grids to mtch the re written in squre rckets. 68 using whole squres only. 65 include hlf squres in your shpe. c 63 include qurter squres in your shpe. d 64.5 include hlves nd qurters. mm cm 4 An rtist hs eight, m, squre-shped pnels which he cn use to mke pttern. The rules for the design re: - the shpe formed cnnot hve ny gps/holes. i.e. or m - it must fit entirely inside the disply pnel shown, - ll the eight pnels must e used in ech design. ow mny different designs cn you come up with? Sketch the min shpes to help you rememer your count. Numer of different designs you found = Mthletics Pssport 3P Lerning 9 5

8 ow does it work? Perimeter using unit squres The word perimeter is comintion of two Greek words peri (round) nd meter (mesure). So finding the perimeter (P) mens mesuring the distnce round the outside! Strt/end of pth round the outside Perimeter( P) = unit+ unit+ unit+ unit = 4 # unit = 4 units Rememer, little dshes on ech side men they re ll the sme length. These exmples shows tht we only count ll the outside edges. Clculte the perimeter of these shpes formed using unit shpes (i) units Strt/end of pth round the outside units Perimeter( P) = units Sides of unit squres inside the shpe not included = 6 units It does not mtter where you strt/finish, ut it is usully esiest to strt from one corner. (ii) 3 units Strt/end of pth round the outside Perimeter( P) = units = 0 units 6 9 Mthletics Pssport 3P Lerning

9 ow does it work? Perimeter using unit squres PERIMETERUSINGUNITSQUARES *PERIMETERUSINGUNITSQUARES * Clculte the perimeter of these shded shpes: Perimeter = units.../.../ 0... = units Perimeter = units = units c Perimeter = units = units Write the length of the perimeter (P) for ech of these shded shpes: c d P = units P = units P = units P = units 3 The shded 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. Mthletics Pssport 3P Lerning 9 7

10 ow does it work? Perimeter using unit squres 4 Drw six ptterns on the grid elow which: ll hve n re of 5 units nd, hve different perimeter from ech other. All squres used for ech pttern must shre t lest one common side or corner point. Drw nother five ptterns on the grid elow which: ll hve n re of 5 units nd, hve different perimeter thn the shpes formed in prt. All squres used for ech pttern must shre t lest hlf of common side point. or corner 8 9 Mthletics Pssport 3P Lerning

11 Where does it work? Are: Squres nd rectngles A simple multipliction will let you clculte the re of squres nd rectngles. For squres nd rectngles, just multiply the length of the perpendiculr sides (Length nd width). Length Length Width Squre Side (x) Width Rectngle Side (y) Side (x) Are = length # width = Side ^xhunits # Side^xhunits = x = x # x units units Side (x) Are = length # width = Side ^xhunits # Side^yhunits = x # = xy y units units ere re some exmples involving numericl lengths: Clculte the re of these shded shpes (i) 4 units Are = length # width = 4units # 4units = 4 units = 6 units So why units squred for re? 4units # 4units = 4 # 4units # units = 4 # units = 6 units (ii) Are = length # width.5 mm = 6mm #.5 mm = 9 mm Units of re mtch units of side length 6 mm All mesurements (or dimensions) must e written in the sme units efore clculting the re. (iii) Are = length # width 60 cm = m # 60 cm = 00cm # 60 cm Write oth lengths using the sme unit m = 000 cm Units of re mtch units of side length Mthletics Pssport 3P Lerning 9 9

12 * AREA: SQUARES* AREA: SQUARES AND RECTANGLES Where does it work? Are: Squres nd rectngles Clculte the re of these squres nd rectngles, nswering using the pproprite units. Are = # units Are = # m length width length width units = units 0.6 m = m c Are = # units d Are = # mm 3 units length width 5 mm length width units = units 3. mm = mm Clculte the re of these squres nd rectngles. Round your nswers to nerest whole squre unit..4 km 7 cm 43 mm AND RECTANGLES.../.../ 0... Are = # km Are = # cm length width length width = km = cm. km (to nerest whole km ). cm (to nerest whole cm ) 3 Wht is the length of this rectngle? Are = 8 units 4 units 4 Wht re the dimensions of squre with n re of m? Psst: rememer the opposite of squring numers is clculting the squre root. 0 9 Mthletics Pssport 3P Lerning

13 Where does it work? Are: Tringles Look t this tringle drwn inside rectngle. eight (Length) Bse (width) The tringle is exctly hlf the size of the rectngle ` Are of the tringle = hlf the re of the rectngle units = of width (se () for tringle) # Length (height (h) for tringle) units = # # h units This rule works to find the re for ll tringles! ere re some exmples involving numericl dimensions: Clculte the re of the shded tringles elow (i) 4 m 5 m Are = # se # height = # 3m # 4m eight = use the perpendiculr height 6 m = 6 m The rule lso works for this next tringle which is just the hlves of two rectngles comined. (ii) 5.4 mm Are = # se # height 4 mm = # 54. mm # 4mm = 0. 8 mm ere, we sy the height is the perpendiculr distnce of the third vertex from the se. For unusul tringles like this shded one, we still multiply the se nd the perpendiculr height nd hlve it. (iii) Are = # se # height = units # 5. units # units = 5. units.5 units Mthletics Pssport 3P Lerning 9

14 Where does it work? Are: Tringles *AREA:TRIANGLES *AREA:TRIANGLES *AREA:TRIANGLES Clculte the re of the tringle tht cuts these two shpes in hlf..../.../ units 8 units units Are = # # units Are = # # units se height se height = units = units Clculte the re of these shded tringles: 4 cm 8 mm cm mm Are = # # mm Are = # # cm = mm = cm c d 0 units 7.5 units 4.5 m 600 cm Rememer: sme units needed. Are = # # units Are = # # m = units = m e Are = # # m 4 m 5 m = m 9 Mthletics Pssport 3P Lerning

15 Where does it work? Are: Prllelogrms Prllelogrms hve opposite sides equl in length nd prllel (lwys the sme distnce prt). Perpendiculr height (h) The shortest distnce etween pir of prllel sides is clled the perpendiculr height We cn mke them look like rectngle y cutting the tringle off one end nd moving it to the other. height Prllelogrm move tringle cut off Rectngle ` Are of prllelogrm = Are of the rectngle formed fter moving tringle = length # perpendiculr height units = l # h units Clculte the re of these prllelogrms (i) Are = length # height 0 mm 5 mm = 30 mm # 5 mm 30 mm = 450 mm A prllelogrm cn lso e formed joining together two identicl tringles. (ii) Find the re of the prllelogrm formed using two of these right ngled 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 nd flip oth verticlly nd horizontlly 5 m Bring them together 5 m Prllelogrm Are = # re of the tringle = # # 5m # m = 60 m OR Are = length # perpendiculr height = 5m # m = 60 m Mthletics Pssport 3P Lerning 9 3

16 Where does it work? Are: Prllelogrms Complete the re clcultions for these prllelogrms: 0 units. cm 3.9 cm AREA: PARALLELOGRAM.../.../ 0... **AREA:PARALLELOGRAM 4.5 mm 4.6 cm Are = # units Are = # cm length height length height = units = cm Clculte the re of the prllelogrms formed using these tringles. 6 m 0 m mm.6 mm 4 m. mm Are = m Are = mm 3 Fill the grid elow with s mny different prllelogrms s you cn which hve n re of 4 units. 4 9 Mthletics Pssport 3P Lerning

17 Where does it work? Are of composite shpes When common shpes re put together, the new shpe mde is clled composite shpe. Common shpe (Rectngle) + Common shpe = (Isosceles tringle) Just clculte the re of ech shpe seprtely then dd (or sutrct) to find the totl composite re. Clculte the re of these composite shpes Composite shpe (Rectngle + Isosceles tringle) Composite just mens it is mde y putting together seprte prts (i) Split into tringle nd squre. 8 cm Are = # cm # 8 cm = 8 cm 0 cm Are = 8 cm # 8 cm = 64 cm 8 cm ` Totl re = Are + Are = 8 cm + 64 cm Add re nd for the composite re cm 8 cm = 7 cm This next one shows how you cn use ddition or sutrction to clculte the re of composite shpes. (ii) 3.5 m method : Split into two rectngles nd 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 cm = 4.5 m ` Totl re = 5.75 m m Add re nd re together = 40.5 m 3.5 m 7 m method : Lrge rectngle minus the smll 'cut out' rectngle 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 Sutrct re from re Mthletics Pssport 3P Lerning 9 5

18 Where does it work? Are of composite shpes Complete the re clcultions for these shded shpes: 6 mm Are = mm # mm Are = mm # mm 4 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 c 6.5 cm cm Are = # cm Are = # # cm.5 cm = cm = cm 6.5 cm cm ` Composite re = - cm 4 cm.5 cm = cm d 5 m Are = # # m Are = # m 3 m m = m = m 5 m ` Composite re = - m = m 3 m m 6 9 Mthletics Pssport 3P Lerning

19 AREA OF COMPOSITEAREA OF COMPOSITE SAPES * Where does it work? Are of composite shpes Clculte the re of these composite shpes, showing ll working: SAPES *.../.../ cm 5 cm cm Are = cm psst: chnge ll the units to metres first. 300 cm 00 cm Are = m 4.5 m c mm Are = mm d psst: this one needs three re clcultions 6 units 0 units 5 units Are = units Mthletics Pssport 3P Lerning 9 7

20 Where does it work? Perimeter of simple shpes By dding together the lengths of ech side, the perimeter of ll common shpes cn e found. Strt/finish Strt/finish Squre width (y units) Rectngle side (y units) Tringle side 3 (z units) side (x units) length (x units) side (x units) Strt/finish P = 4 # side length P = width+ length+ width + length = 4 # x units = ^y+ x+ y+ xh units = 4x units = ^ # xh+ ^ # yhunits = x+ yunits ere re some exmples involving numericl dimensions: P = side + side + side 3 = x+ y+ z units You cn strt/end t ny vertex of the shpe Clculte the perimeter of these common shpes (i) s 8 units s 8 units Sum of ll the side lengths 0 units Strt/finish 0 units Perimeter = units + 8units+ 0 units = 9 units (ii) Strt/finish.3 cm.3 cm.3 cm Four lots of the sme side length.3 cm.3 cm Perimeter = 4 # 3. cm = 9. cm All mesurements must e in the sme units efore clculting perimeter. (iii) The perimeter for prllelogrms is done the sme s for rectngles. Clculte this perimeter in mm. 5 mm 5 mm Strt/finish 0.5 cm 5 mm 5 mm All side lengths in mm 5 mm Perimeter = # 5mm+ # 5 mm = 30 mm + 0 mm = 40 mm Opposite sides in pirs 8 9 Mthletics Pssport 3P Lerning

21 Where does it work? Perimeter of simple shpes Complete the perimeter clcultions for these shpes: OF SIMPLE SAPES * PERIMETER OF SIMPLE SAPES * PERIMETER..... /..... / units Perimeter = units + units + units 5 units 8 units = units c 6 mm 9 mm Perimeter = # mm + # mm = mm Perimeter = # m 5 m = m d cm 5 m Perimeter = # cm + cm = cm Clculte the perimeter of the shpes elow, using the spce to show ll working: 5 m 5.8 cm Perimeter = cm Perimeter = m c d.6 mm 3 m 5 m 3.4 m.4 mm.6 m.4 m Perimeter = mm Perimeter = m Mthletics Pssport 3P Lerning 9 9

22 Where does it work? Perimeter of simple shpes 3 Find the perimeter of ech shpe written using the smller units of mesurement in ech digrm. in cm. in mm. 550 cm 3 m 600 cm 6.5 cm 5 mm Perimeter = cm Perimeter = mm 4 Ech shpe elow hs its perimeter written inside nd is missing one of the side length vlues. Rule stright line etween ech shpe nd the correct missing side length on the right to nswer: ow mny stright sides does n icosgon hve? 4.4 m P = 4 m 5. m P = m F d E c V L N T 8 m.4 m 3.5 m 380 cm P = 3 m 9 m W S v 440 cm m P = 4 m 6.5 m P = 8 m m N v E c Y T R c G d 7 m 650 cm. m 6 m.6 m P = m 5 m c d m v 0 9 Mthletics Pssport 3P Lerning

23 Where does it work? Perimeter of composite shpes The lengths of the unlelled sides must e found in composite shpes efore clculting 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. Clculte the perimeter of these composite shpes (i) 9 cm cm 30 mm 9 cm 5 cm cm 3 cm Clculte ech side length of the shpe in the sme units 9 cm + 5 cm = 4 cm ` Perimeter = 9cm+ 3cm+ 4cm+ cm = 48 cm (ii) 3 m You cn lso imgine the sides re-positioned to mke the clcultion 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 Mthletics Pssport 3P Lerning 9

24 Where does it work? Perimeter of composite shpes Clculte the vlue of the sides lelled nd in ech of these composite shpes: 3 m cm 8 cm = cm = cm. mm mm 3.4 mm =.6 mm = mm mm c 8 m 5 m = = m m d 4 cm 5 cm 4.8 cm 8 cm = = cm cm 5 cm Clculte the perimeter of these composite shpes: Perimeter = # cm 9.8 mm = cm PERIMETER OF COMPOSITE SAPES * PERIMETER OF COMPOSITE SAPES * m Perimeter = # m + # m 3.../.../ 0... m 4 m = m + m Be creful with the units for these next two = m c. cm 6 mm 0 mm Perimeter = 3 # mm + mm + mm = mm d 4. cm 38 mm Perimeter = # 4. cm + # cm = cm 9 Mthletics Pssport 3P Lerning

25 Where does it work? Perimeter of composite shpes 3 Clculte the perimeter of these composite shpes in the units given in squre rckets. Show ll working. 6 mm@ 6 m@ 4 mm. m Perimeter = mm Perimeter = m c 6 cm@ 48 mm d 6 km@ psst: km = 000 m.5 km 3.6 cm mm 00 m Perimeter = cm Perimeter = km 4 Ern n wesome pssport stmp for this one! The incomplete geometric pth shown elow is eing constructed using comintion of the following shped pvers: m m m m m.4 m.4 m m The gp in etween ech prt of the spirl pth is lwys m wide. Clculte wht the totl perimeter of this pth will e when finished. Completed pth m m AWESOMEAWESOME AWESOMEAWESOME AWESOME AWESOME.../.../ 0... Totl perimeter of completed pth = m Mthletics Pssport 3P Lerning 9 3

26 Where does it work? Perimeter of composite shpes 5 The four composite shpes elow hve een formed using five, unit squres. Using your knowledge of perimeter nd the grid elow, comine ll four pieces to crete two different shpes so tht: One shpe hs the smllest possile perimeter. The other hs the lrgest possile perimeter. All shpes must e connected y t lest one whole side of unit squre. Briefly descrie the strtegy you used to chieve ech outcome elow: A shpe with the smllest possile perimeter. A shpe with the lrgest possile perimeter. 4 9 Mthletics Pssport 3P Lerning

27 Where does it work? Simple word prolems involving re nd perimeter Sometimes we cn only communicte ides or prolems through words. So it is importnt to e le to tke written/spoken informtion nd turn it into something useful. For exmple, Miguel wnts to pint squre. e hs just enough pint to crete line 40 cm long. Wht is the longest length ech side of the squre cn 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 cm. So ech side length = 40cm ' 4 = 60 cm ` The longest length ech side of the squre pinted y Miguel cn e is 60 cm. This is useful for Miguel to know ecuse if he pinted the first side too long, he would run out of pint! ere re some more exmples (i) A rectngulr prk is four times longer thn it is wide. If the prk is 90 m long, how much re does this prk cover? ^90 ' 4hm =.5 m Drw digrm to illustrte prolem (ii) 90 m Are = length # width = 90 m #.5 m = 05 m At fun run, competitors run stright for 0.9 km efore turning left 90 degrees to run stright for further. km. The course hs one finl corner which leds ck to the strt long stright.5 km long street. ow mny lps of this course do competitors complete if they run totl of 8 km?. km.5 km 0.9 km Drw digrm to illustrte prolem Strt/finish Perimeter ofcourse = 0.9km+. km+.5 km = 3.6 km Perimeter will e the length of ech lp ` Length of ech lp of the course is 3.6 km ` Numer of lps = 8 km' 36. km Rce distnce divided y the length of ech lp = 5 ` Competitors must complete 5 lps of the course to finish Mthletics Pssport 3P Lerning 9 5

28 Where does it work? Simple word prolems involving re nd perimeter Three equilterl tringles, ech with sides of length 3 cm hve een plced together to mke one closed four-sided shpe. Ech tringle shres t lest one whole side with nother. Clculte the perimeter of the shpe formed. Use ll four squres elow to mke two shpes in which the numer of sides is lso equl to four. Compre the distnce round the outside of your two shpes nd explin wht this shows us out the reltionship etween re nd perimeter. You hve een employed y fric design compny clled Doule Geometrics. Your first tsk s pttern mker is to design the following using ll seven identicl squres: Closed shpes for new pttern in which the vlue of their perimeter is twice the vlue of their re. Drw five possile different ptterns tht mtch this design request. 3 The se length of right-ngled tringle is one fifth of its height. If the se of this tringle is 4. m, clculte the re of the tringle. SIMPLE WORD PROBLEMS INVOLVING AREA AND PERIMETER.../.../ Mthletics Pssport 3P Lerning

29 Where does it work? Simple word prolems involving re nd perimeter 4 An rchitect is sked to design n rt gllery uilding. One of the design rules is tht the floor must e rectngle shpe with n re of 64 m. If only whole metre mesurements cn e used, sketch ll the different possile floor dimensions. Another design rule is to try ensure lrge perimeter so there is more spce to hng pintings from. Use clcultions to show which floor pln will hve the lrgest perimeter. c Would the design with the lrgest possile perimeter e good choice? Explin riefly why/why not. d A smll rt piece t the gllery hs one side of n envelope completely covered in stmps like the one pictured elow. ow mny of these stmps were needed to cover one side of n envelope.5 cm wide nd 4.5 cm long if they ll fit perfectly without ny edges overlpping?.5 cm 3.5 cm.5 cm 4.5 cm Mthletics Pssport 3P Lerning 9 7

30 Where does it work? Simple word prolems involving re nd perimeter 5 A fence used to close off prllelogrm-shped re is eing rerrnged to crete squre re with the sme perimeter. The short side of the re is 34 m long (hlf the length of the long side). ow long will ech side of the new squre re e fter using the whole length of this fence? 34 m 6 If the distnce etween the longer sides of the originl re ws 30 m nd the length did not chnge, use clcultions to show which fencing rrngement surrounded the lrgest re. A wll is creted y stcking equl-sized rectngulr ricks on top of ech other s shown. The end of ech rectngle sits exctly hlf-wy long the long side of the rectngle underneth it. Ech rick = 6 cm 8 cm 8 A 500 ml tin of white pint hs een purchsed to pint the wll. The instructions on the pint tin sy this is enough to cover n re of 500 cm. Use clcultions to show tht there is enough pint in the tin to cover side of the wll. If eetle wlked ll round the outside of the wll (including long the ground), how mny metres did it wlk? 9 Mthletics Pssport 3P Lerning

31 Wht else cn you do? Rhomus nd Kite shpes The re for oth of these shpes cn e clculted the sme wy using the length of their digonls. A B A Rhomus is A rhomus is like squre prllelogrm. prllelogrm, so Are = ^digonl lengths multipliedtogetherh ' we cn lso use the sme rule to D C = ^AC # BDh ' find the re: A B C Perimeter = 4 = # 4 # AB lengthofone side length A kite hs two pirs of equl sides which re djcent (next to) ech other. Are = ^digonl lengths multipliedtogetherh ' height = ^AC # BDh ' D Perimeter = # short side + # long side = AB + # # ere re some exmples: Clculte the re nd perimeter of these shpes AD (i) For this rhomus, WY = cm nd XZ = 6 cm. W X Are = ^digonl lengths multipliedtogetherh ' = ^ cm # 6 cmh ' Z 0 cm Y = 96 cm Perimeter = 4 # lengthofsides = 4 # 0 cm = 40 cm (ii) For the kite ABCD shown elow, AC = 4.7 m nd BD =. m. A.5 m B 3.7 m Are = ^digonl lengths multipliedtogetherh ' = ^. m # 47. mh ' = m D C Perimeter = # short side + # long side = # 5. m+ # 3.7 m = 0.4 m Mthletics Pssport 3P Lerning 9 9

32 Wht else cn you do? Rhomus nd Kite shpes Clculte the re nd perimeter of these shpes: PR = 8 cm nd QS = 5 cm Q BD =.8 mm nd AC =.4 mm.../.../ 0... RROMBUS AND KITE SAPES OMBUS AND KITE SAPES 4 cm A B P S R 5 cm D 3.6 mm C Are = # ' cm = cm Are = # # mm = mm ' = # Perimeter = # + # cm Perimeter = # mm = cm = mm Clculte the perimeter of these composite shpes: 4 m 6.5 cm 3.4 cm 9 m 5. cm Perimeter = m Perimeter = cm 3 Clculte the re of this composite shpe, showing ll working when: J L = 30 m, IK = IM = 6 m nd JL = m I K M L Are = m 30 9 Mthletics Pssport 3P Lerning

33 Wht else cn you do? Trpezoids A trpezoid is qudrilterl which hs only one pir of prllel sides. So the re formul for trpezoid would lso work on ll of those shpes. A B A B height (h) height (h) C D C D Two common trpezoid shpes In oth shpes, the sides AB () nd CD () re prllel ( AB CD ). The height is the perpendiculr distnce etween the prllel sides. : Are = ^sumofthe prllelsidesh # height ' = ^+ h # h ' : Perimeter = AB + BD + CD + AC ere re some exmples: Clculte the re nd perimeter of these shpes (i) 0 mm Are = ^sumof the prllelsidesh # height ' = ^ mm + 0 mmh # 6 mm ' = 3 mm # 6 mm ' 0 mm mm = 56 mm 6 mm Perimeter = 0 mm+ mm+ 6 mm+ 0 mm = 68 mm (ii) 6.7 m Are = ^sumof the prllelsidesh # height '.9 m m 4.5 m 0. m = ^67. m+ 4. 5mh # m ' =. m # m' =. m Perimeter = 67. m+ 0. m+ 45. m+ 9. m = 34. m Mthletics Pssport 3P Lerning 9 3

34 Wht else cn you do? TRAPEZOIDS * TRAPEZOIDS * TRAPEZOIDS * TRAPEZOIDS * Trpezoids Clculte the re nd perimeter of these trpezoids: km.5 m.../.../ km 9 km 4 km.8 m 8. m 53 km 4.5 m Are = + # ' km Are = + # ' m = km = m Perimeter = km Perimeter = m Use the trpezoid method to clculte the re of these composite plne shpes. 8 cm 5 cm mm.4 mm 4.3 mm 5 cm Are = cm Are = mm 3 Use the trpezoid method to clculte the re of this composite plne shpes. 6.7 m 33.4 m 70 cm 40 cm Are = m Perimeter = m 3 9 Mthletics Pssport 3P Lerning

35 Wht else cn you do? Are chllenge Fill the grid elow with s mny different squres, tringles, rectngles, prllelogrms, rhomi, kites nd trpezoids s you cn which ll hve the sme re of 8 units. Mthletics Pssport 3P Lerning 9 33

36 Wht else cn you do? Reflection Time Reflecting on the work covered within this ooklet: Wht useful skills hve you gined y lerning how to clculte the re nd perimeter of plne shpes? Write out one or two wys you think you could pply re nd perimeter clcultions to rel life sitution. If you discovered or lernt out ny shortcuts to help with clculting re nd perimeter or some other cool fcts/conversions, jot them down here: 34 9 Mthletics Pssport 3P Lerning

37 Chet Sheet ere is wht you need to rememer from this topic on Are nd perimeter Are using unit squres Are is just the mount of flt spce shpe hs inside its edges or oundries. A unit squre is squre with ech side exctly one unit of mesurement long. Count the totl numer of whole squres, or frctions of squres to clculte the re. Are (A) = units Perimeter using unit squres The perimeter with unit squres mens count the numer of edges round the outside of the shpe. Perimeter (P) = 6 units Are: Squres nd rectngles Just multiply the length of the perpendiculr sides (length nd width). length length width Squre side (x) width Rectngle side (y) side (x) Are = length # width = x units side (x) Are = length # width = xy units Are: Tringles height height height Are: Prllelogrms se se se ` Are of the tringle = (hlf the se multiplied y the perpendiculr height) units = # # h units Perpendiculr height (h) Length (l) ` Are of prllelogrm = length # perpendiculr height units = l # h units Mthletics Pssport 3P Lerning 9 35

38 Chet Sheet Are of composite shpes + Are (Rectngle) + Are = (Isosceles tringle) Composite Are = Are + Are (Rectngle + Isosceles tringle) Perimeter of simple shpes Add together the lengths of every side which mke the shpe. Strt/finish Strt/finish Squre width (y units) Rectngle side (y units) Tringle side 3 (z units) side (x units) length (x units) side (x units) Strt/finish P = 4 # = 4x units side length P = width+ length+ width + length = x+ yunits P = side + side + side 3 = x+ y+ z units Perimeter of composite shpes The lengths of ll unlelled sides must e found in composite shpes efore clculting their perimeter. It is esier to dd 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 nd Trpezoids 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 perpendiculr height (h) D A C Are = ( + ) # h ' Perimeter = AB + BD + CD + AC perpendiculr height (h) Trpezoid B D 36 9 Mthletics Pssport 3P Lerning

39

40