The area of a square is found by using the formula A = l 2, l
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1 To clcult t r o t prlllogrm, irst rw igonl rom B to D to orm two tringls, ABD n BDC. Ll t s, n t prpniculr igt,. Tn in t r o t two tringls. T r o tringl A B BCD = 1 2 ì n t r o tringl ABD = 1 2 ì. D C So, t r o t prlllogrm ABCD = 1 2 ì ì A B = ì For xmpl, t r o t prlllogrm sown t rigt is: Ar ABCD = ì = 6 ì 4 = 2 2 D C rmmbr XrCis 9 individual PtHWys Book plus s Activity 9-D-1 Ar oc-1864 Activity 9-D-2 Mor r oc-1865 Activity 9-D-3 Avnc r oc T r o sp is t mount o lt surc nclos y t sp. 2. Ar is msur in squr units suc s mm 2, cm 2, m 2 n km Lrg rs o ln r otn msur in ctrs. 1 = m Ar my oun y counting t numr o squrs n to covr surc. 5. A squr wit si msur o 1 cm s n r o 1 squr cntimtr (1 cm 2 l ). 6. T r o rctngl is oun y using t ormul A = lw, w wr A is t r o t rctngl, l is its lngt n w is its wit. 7. A squr is rctngl wos lngt n wit r qul. l T r o squr is oun y using t ormul A = l 2, wr l is its si lngt. l 8. T r o tringl is qul to l tt o rctngl wit t sm s n igt. 9. T r o tringl my oun using t ormul A = 1 2, wr is t s n is t igt o t tringl. 10. T r o prlllogrm is: A = wr is t lngt o t s n is t prpniculr lngt o t prlllogrm. r luncy 1 Wic unit woul most suitl to msur t ollowing rs? Coos rom mm 2, cm 2, m 2, or km 2. A computr scrn A st o A3 ppr c Mlourn Crickt Groun A sirt utton T Mlourn mtropolitn r A compct isc g A ous lock A room i Alsk j A sktll court k A iry rm l T r insi t lttr D 2 W7 T igurs low r rwn on cntimtr gri ppr. Fin t r o c on. c Cptr 9 Msurmnt 315
2 Bookplus Intrctivity Ar plus workst int W7 Fin t r o t igurs low, wic r rwn on cntimtr gri ppr. c g 4 W8 Estimt t s r o c o t ollowing igurs i c is rwn on cntimtr gri ppr. c 5 Four rctngls r rwn on cntimtr gris tt ollow. i Stt t lngt n wit o c rctngl. ii Us your nswrs to prt i to clcult t r o c rc tngl. iii Count t numr o 1-cm 2 squrs to in t r o c rc tngl. iv Compr your nswrs to prts ii n iii. 316 Mts Qust 7 or t Austrlin Curriculum
3 c 6 W9 Fin t r o t ollowing rctngls. (Hint: Us t ormul A = lw.) 5 cm c 3 m 1 cm 3 cm 5 m 7 km 2 km 5 m Book plus s Digitl ocs Sprst Ar o rctngl oc Accurtly msur t lngt n wit o c rctngl in t units spcii y t rckt. Hnc, clcult t r o t rctngl. (cm) (cm) c (mm) (mm) (cm) (mm) 8 W9,c Fin t r o t ollowing sps. (Hint: Divi t sps into rctngls n squrs or using t ormul A = lw.) 8 m 1 8 m Cptr 9 Msurmnt 317
4 c 21 mm 8 m 4 m 15 mm 4 m 9 mm 6 mm 1 3 cm 9 cm g 1 5 cm 4 m 6 m 6 m 5 cm 3 cm 1 cm i 9 mm j 7 mm 1m 15 mm 3 mm 3 mm 3 mm 28 mm 35 mm 21 mm 7 mm 9 W10 Fin t r o t ollowing tringls. 3 cm c 9 cm 9 cm 5 cm 1 cm 8 cm 20 cm 318 Mts Qust 7 or t Austrlin Curriculum
5 10 MC In t igrm sown t rigt, t igt o t tringl is: A 60 mm B 30 mm C 27 mm D 53 mm E 49 mm In t igrm sown t rigt, t igt o t tringl is: A 2. B 4.0 cm C 3.0 cm D 4. E 3.8 cm 30 mm 53 mm 27 mm 60 mm 4.0 cm 2. c In t igrm sown t rigt, t 7. s lngt o t tringl is: A 4.1 cm B 2.9 cm 2.9 cm 4.1 cm C 5.3 cm D cm E 7.0 cm In t igrm sown t rigt, t s lngt o t tringl is: A 39 cm B 58 cm C 29 cm D 25 cm E 43 cm 39 cm 3.0 cm 58 cm Book plus s Digitl ocs Sprst Ar o tringl oc-1877 T r o t tringl sown t rigt is: A B 9. 2 C 1 2 D 15 cm 2 E W11 Fin t r o c o ts tringls m 3. 5 cm c 2.5 m 29 cm 25 cm g 3.0 m 40 km 1.6 m 51 mm 29 mm 34 mm 25 cm i 28 cm 19 cm cm 57 cm 50 km 30 km 27 cm 1 12 Dtrmin t r o t prlllogrm sown t rigt. B A 13 T tl low givs t ss, igts n rs o vrious prlllogrms. Complt t tl. Bs Higt Ar 5 mm 3 mm 8 cm 5 2 c km 2 km 1200 mm m 8.7 m 4.m C 6.7 mm D Cptr 9 Msurmnt 319
6 MsurMnt n gomtry Using Units o MAsUrMnt UnDrstAnDing 14 Estimt t r o t sils o tis yct Estimt t r o tis uttrly i i mtr gri is ovr it s sown. cntimtr gri is ovr it s sown. Estimt t r o t cocolt scoop in tis pictur o n ic-crm i cntimtr gri is ovr it s sown. c Estimt t r o Austrli i 470 km gri is ovr it s sown. Not: T r o c squr o t gri is 470 km ì 470 km or km2. Nortrn Trritory Commonwlt control 1911 Sl-govrnmnt 1978 Wstrn Austrli Qunsln Sout Au n pitl pit Trritor y 15 On o t lrgst opn-ir sopping cntrs is t Al Mon cntr in Honolulu, Hwii, USA wit mor tn 200 sops covring n r o 20 ctrs. How mny squr mtrs is tis? T Tupo volcnic ruption, in Nw Zln nrly 2000 yrs go, is stimt to v lttn n r o km2. How mny squr mtrs is tis? How mny ctrs is tis? How mny squr mtrs o crpt r n to crpt rctngulr room o lngt 5 m n wit 3.5 m? Fin t r o mtril (cm2) n to mk rctngulr tl npkin 3 long n 25 cm wi. Fin t r o mtril n to mk rctngulr rug wic is 4. long n 230 cm wi. (Giv your nswr in squr mtrs.) (Hint: Convrt t wit msurmnt into mtrs irst.) Mts Qust 7 or t Austrlin Curriculum
7 20 Toy is tiling is troom wit crmic tils tt cost $35.20 pr ox. How mny squr mtrs o tils will n, i t rctngulr room s wit o 2.5 m n lngt o 3 m? How mny oxs o tils soul orr i c ox contins noug tils to covr 0.5 m 2? c Wt will t cost o t tils? 21 Jn is lnscp grnr wo is lying nw lwn. T rctngulr lwn is 13 m long n 8 m wi. How mny squr mtrs o tur soul Jn orr? Wt is t totl cost o t tur i it costs $12.50 pr squr mtr? 22 Aln, wo works or Fst Glss Rplcmnts, s n sk or quot to rplc tr winows. Ec winow is 1.8 m long n 0.8 m wi. Wt pric soul Aln quot i t glss costs $27 pr squr mtr? (Inclu livry cost o $25 in t quot.) 23 Fin t totl r o t cttl sttion sown t rigt, 36 km 24 km wic s 3 lrg pocks. (Giv your nswr in squr 48 km kilomtrs.) 24 Rctngulr lmint sts r 1.8 m long n 0.9 m 34 km 120 km wi. How mny sts woul n to covr 4.8 m 2 o nc spc in kitcn? 8 m 25 Clcult t totl loor r o concrt sl or ous s sown t rigt. 26 How mny squr cntimtrs o cror r n to mk t cu wit n g lngt 9 m 7 m o 1 sown t rigt m 27 Clcult t pproximt r o t tringulr minsil wn t sil is lt. Us t imnsions sown on t yct t rigt. 28 Wt r o clot woul rquir to mk on o t pnnnts sown low? 48 m 3.7 m 40 cm 45 cm Cptr 9 Msurmnt 321
8 80 cm MsurMnt n gomtry Using Units o MAsUrMnt 29 Fin t r o clot rquir to mk t kit sown, givn tt t lngt BD is 80 cm n t lngt AC is 1.5 m. B C 1.5 m D A 30 A curc spir s six inticl tringulr cs tt v t imnsions sown t rigt. Wt r o coppr rooing woul rquir to covr ll six cs o t spir? 4. 1 m 31 Fin t totl wing r o t lt wing jt ircrt sown low. 18 m 7 m 7 m 32 T tringl sown low cn us to mk n stimt o t r o t stt o Vic tori. 500 km 850 km Fin t r o t tri ngl sown. Compr your stimt wit t corrct vlu rom your tls. rasoning 33 A loor tilr crg $ to til rctngulr room. Hr nxt jo is to til t loor o rctngulr room twic s long n twic s wi. How muc soul s crg or t lrgr room? (T nswr is not $ ) 322 Mts Qust 7 or t Austrlin Curriculum
9 34 A rctngl s n r o 3 2 n primtr o 2. Ec si o t rctngl is wol numr o cntimtrs. Wt is t lngt n wit o tis rctngl? 35 Wt is t primtr o squr tt s t sm r s rctngl wit lngt 18 mm n wit 8 mm? rlction Nm som ojcts rom your immit surrounings wos r you cn in using t ormul or t rs o rctngls, squrs n tringls. 9 Ar o composit sps, using ition n sutrction Composit sps cn ivi into prts, c o wic is simpl sp (suc s, or xmpl, rctngl or tringl), wos rs r sy to in using milir ormul. T r o composit sp cn oun y ing t rs o c prt o t ivi sp. For xmpl, t r o t pntgon sown low cn oun y ining n tn ing t rs o t tringl n rctngl. WorK XMPL 12 Fin t r o t sp t rigt. 7 cm 1 think Writ 1 Divi t sp into rctngl n tringl. 7 cm cm 2 Us t ormul A = lw to in t r o t rctngl. 3 Us t ormul A = 1 to in t r o t 2 tringl. Ar 1 = lw = 7 ì 4 = 28 cm 2 Ar 2 = 1 2 = 1 2 ì 5 ì 4 = 10 cm 2 4 A t two rs to gt t totl r. Totl r = A 1 + A 2 = = 38 cm 2 Cptr 9 Msurmnt 323
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