P3@   Sl$ l0C)HCC WhL/h `CmCDiD`  R@W1  Y0@R !L` D  C D     )16CS S)  C)D1 p p 0 C9DI pCDL~CiCDiD`HAYDEN SOFTWARE( SCORE IMPROVEMENT SYSTEM FOR THE SATA. System User's Guide:B. Complementary, Supplementary Angles And Angle SumsC. Parallel LinesD. Angles Of A Circle"E. Equalities Of Angles And SidesF. Pythagorean TheoremG. Special TrianglesH. Perimeters I. AreasJ. Similar Figures K. Volumes"L. All Examples Without TUTORMODEA. Using The GEOMETRY MODULEB. Organization Of The System MAIN MENU Detail MenuPROGRAMREVIEW'M = Main Menu Q = Quit R = Restart M = Menu | = Back'R = Restart M = Menu O = Omit | = BackP = Paragraph Q = QuitPx X`H232435; 1 ;  hh@2 e1i1L;Hҍ 00) 08 109hh@ 2e1i1232435ޥ<<8=LxLLLLLLL LL: LT LL_ L L L L ! h`LL6 LLL LhLJLTLLLLLLL&LN LL ! v 5 7 h` Ltv W h`h  ` v 5 v h` v v v v Lx  v [ v h`t v 8 v [ v v h`v   7 Nh`Y sLw ! v Lr  7 A[08!sh`v h`  v 5 h` v W v  ]h` v v h` v v v v >v`h0BJKՅԩ3D ELVK:h0BHI V`hhhhhhh΢ e˅ː`˪8包˥卅̩***ΥeͥeΠˑȥ̑Ȋȩ`h h       i  w  L l wv   ` ӠŠҠϠ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ]  ] ] ] ҠӠͧϠנΠϠŠҠҺENTER YOUR NEW ANSWERϠŠҠҠĺENTER YOUR PREVIOUS ANSWER Ϡՠ٠ԠϠԿ٬ΩӠҧϠנŠӠէϠנĠӠçϠӠӧϠ ҠӠŠҠϠ ŠҠϠ ԠŠƠŠŠ  RAW SAT TIME SCORE SCORE REMAININGENTER TOTAL OF PREVIOUSLY RECORDED DATA  ĠӠ ƠՠȠϠŠŠĠŠ VERBAL NUMBER CORRECT = VERBAL NUMBER INCORRECT = MATH NUMBER CORRECT = MATH NUMBER INCORRECT = ҠԠӠΠϠhPͩΩ vw'u vt$hPͩgΩ̢Pvw`   ` vHwH)8w hwhv` (wLO ˑΥPɚ` v` w` t`  |`έ͠ ɛLv LOL u k'u`     HL `8Ii8HhIi J`m 8 Ln,8`,`jnNN)P˩gȈ i(ː `@ hhh hHH` j H h`v8`)0i(mw j  fjfj(j`vw(wv`έ) & &΅ͦνi`w,I˥i(ː`ˮvʊ mvJfJf˅̢,ue˅˽e̅`PPgѩi  PR 0m `  0έͩP˩̩@Ѡ075Ȍ 2ˬȌ  e˅ːвˍȱˍL խ ` L/ =`ɛ& `!ɛέ `Lɛ ڭ...eͭeΠȩͩ`ЩP  K``P ` `ϩЩ`fff1j$$$$>`<|fl0fF0p88p``~0~ 0`@ 80 @~~`0 0```nf>ff~fff~~f<flxxlf`````~cwkccfv~~nf8pp8?ww<~~~<x`x`~<~~<0~0 ~ <>f>``|ff|<```<>ff>>ff>|``|fff8<<``lxlf8<fkc|ffffff>|f```>`<|~ffff>fff<ck>6f< x~ 0~$B00fff S`ѩ Pυ˩Ѕ 0 P `L}) ȱˍ 0ȑˍm mː` ˩ȱ)ȩˍ8` ˍ ȱˍ  `  ȭ  `ˍ̍˭`˭`P̢ѱϑ `P˩̩Тѱˑ`` #mm P˩ 0 P `m 8J P˩ 0 P`H232435; 1 ;  hh@2 e1i1L(Hҍ 00) 08 109hh@ Ҡ2e1i1232435ޥ<<8hl˩l̠e˅ː`hҢҩyҍ* \*`h, \`&%8%0%## # # ## #@#"!@!`! ! !0!!!!!!!!!!!!! ! !`!@!""@#`#0# # # #$@%0%8%&7Ȍ!E`Ȍș`[ȌHșhL`LOAD "D:GEOM.BAS"RUNh@} DR a   x X) L S` i`A}7Ȍ!E`Ȍș`[ȌHșhL`LOAD "D:GEOM.BAS"RUNhPg p} @ЩѠxeЅАeЅАѹkI(eЅАѹk8аѹk(eЅАѹk C}(eЅАѹkPeЅАѹk(eЅАѹk(eЅАѹlЈ(eЅАѹlЈ(eЅА D}ѹlЈ(eЅАѹ.lЈ@ЩѠ(eЅАшeЅАѠ =lЈ eЅАйIlЈWeЅАѹjlЈ$e E}Аѹ|lЈ3ЩѩͩΩMЩN͈ТEͩΩBЩV(eЅА(e͐ͅ ݠ؅Щ8nj Јkjljmj F}kjkjljlj} ЩѠk8 IЈѩйk8 IЈЩѹvj8 󩰅Ѡ!fk8 ЈU  R G}  $%& S0 S0 &%&$8Dkjljkjljlj} bdpe H}jk Vbde hi V0L^jLGEOMETRY* "SAT" AND "SCHOLASTIC APTITUDE TEST"ARE REGISTERED TRADEMAR I}KS OF THE COLLEGEENTRANCE EXAMINATION BOARD. THESEMATERIALS HAVE BEEN DEVELOPED BY ARROWINSTRUCTIONAL SYSTEMS, INC. J} FOR HAYDENSOFTWARE COMPANY, INC. WHICH BEARS SOLERESPONSIBILITY FOR THEIR CONTENTS.ATARI CONVERSIONBY ANDREW TAYLOR(!9$%.3 K}/&47!2%3#/2%NNNNNNNNNN)-02/6%-%.4NNNN3934%-&/24(%NHJHJ JHJYʀJYʀJYʀY L}ʀY$%6%,/0%$"9!22/7).3425#4)/.!,3934%-3 ).##/092)'(4# "9(!9$%.3/&47!2%#/ ).##).#3830 ;384 M}0 CHK2 STY TIMER ;timer =13850 JSR DSKINV ;do a read...3860 BMI ERROR ;stop fo}r any err3870 LDA TIMER ;wi N}thin time limit?3880 CMP #8+13890 BCS CHK3 ; no!3900 DEC TESTCNT ;yes, dec t}est cnt3910 CHK3 DEC CURRCNT O}3920 BNE CHK2 ; test more intervals3930 LDA TESTCNT ;all intervals OK?3940 CLC }; assume all is OK395 P}0 BEQ ACCEPT ;Yes, accept: PROTECTED3960 DEC RTRYCNT ;else, re-try Op3970 BNE CHK13}980 ERROR SEC ; Give Q} up!3990 ACCEPT BCC WAIT4000 LDA #$FF4001 STA $02444010 JMP $E4774020 WAIT LDA #04030 STA T}IM4040 STA TIM+140 R}50 TAX4060 WAIT1 INX4070 BNE WAIT14080 INC TIM4090 BNE WAIT14100 INC TIM+14110 LDA TIM+1412}0 CMP #184130 B S}NE WAIT14140 LDA #04150 STA $02F04160 LDA #$7D4170 JSR $F6A44180 LDA #34190 STA IOCB+24200 D:AUTORUN.BAK210 ST T}A IOCB+44220PgЩѠxeЅАeЅАѹkI(eЅАѹk8аѹk(eЅАѹk xY#k#MNDNFXABBLBSCDEFMPRRESCANF1F2F3FLINTTLTXDSSCSKTMCPPMERWRSRRTSWCPXYV}YLNXXOORRRVRHRISPCASQQFMMFTMTVDMVDVRCTW} X}@@@ !"#$Y}%&'()*+,-./01234Z}56789:;<=>?@ABC[}DEFGHIJKLMNOPQRS\}TUVGEOMETRY, A0"F:@, A(, @A"@+F:@,&A(,AB7]}t+F:B7t,&A(, ss;@`,;@,;@@,;@,;@,;@,;@,;@,;@^},;@, ss;@,;@,;@,;@,;@',;@,;@,;@,;@,;@_},GG;@,;@,;@`,;@`,;@`,;@,669@<@,9@E<@,9@`},6-?:AQ,) +@@)AV@ Q0@@ @70@@Q0@a}@ @"F:@, A(" @%A"@+F:@,&A(,AB7t+F:B7t,&A(, b}A"P A!0!T 6-?:,6-!6-?:A a,+ A J?:A!Q#8<,"68<,-d}# @u@'8<,"6-?:A d,' @uB"8<, Au" @uD- 6-% A #7<,4~S- @he}G 6-&K  @N @ @PP 6-% A R "6-$T7<,4~ A Z f}" $n, 6. A"6-?:A!E,, @x 4~RA AP 4~RC A 7<,4~Q6-?:,g}$ 0~SD Ap$6-?:A d,6-$6-"8<,%68<,- @ 0~SB A`h}! 6-"8<,%!68<,-38<,%6-6-?:,) Ay3 @ Au @/ 6-6-?:,i}6-8<,)")"%/6- 6- 6-% A " 46-?:A ,"6.~SP! 4~SP A ! Ayj} 0~SG A0 A(-@$6-?:<<<<,( (-@$6-?:<<<<,( /6-?:k}<<<<,%6-?:<<<<,/ Ay56-+A:7<%,,,$'56-A:7@<@%,,G%6-+A:7@<@%,,,$l}'G6-+A:7@<@%,,,$';6-A:7@<@%,,;6-A:7@<@%,,$ A 6-$m}'6-$'A%6-+A:7@"<@"%,,,$'A6-A:7@%<@%%,,6-?:<<<<<<<<,$ 0~SH n}A@)6-?::8<,,467B:,%@,.'*6-?:<@ ,4 A?6.7<,6-?:<@!,?6.SELECT THE COt}RRECT ANSWER A A0" $4)4EEA A  4*" A 0O A  6-u} "6- "6-?:<, A ) 6-?:,68<,-8<,%)68<,- @ 2)3 A v} "6-  6- "6-?:<, A 68<,-@:,0 0 A: 68<,- 68<,-8<,%D26w}-?:<@ ,26.CORRECT, THE ANSWER IS IA67B:,%@,.-67B:,%@,.'7 AA APN 68<,- 6x}8<,-8<,%X-6-?:<@ ,-6.THE CORRECT ANSWERY167B:,%@,. IS '167B:,%@,.Z-67B:,%@y},.'# A- APb#+2Q)3,*0*0# Av 6- 0Q A A" APz} A  0 A 6-6-?:,$ 6-&"6-?:,$ @4 A 4~SB)4~SD.6-?:A {}d,46-7<,0~Q A`%6-A:7<+B:,&,%,,%6-8<, " AV AX+68<,-8<|},& 8<, +68<,- 6-&6-7<,0~R A  "6-?:, @  6- A  0}} A'6-?:A d,6-"$6-'$ A 5 6-?:,-@E"--68<,-1 5 ,-~}@-$68<,-( , 0 6-6-6-6-!6-'6--6-0$ 4)4~ET6-* "6-?:,}$4 6-?:, @>AdAUR"F:Ad,"AU" AP\6.>:?:A!,,$;'?:A!<<@$} AG6-?:,V6-?:A!E,Z6-?:<@$,#6-?:<<<,)6.3 A<6-?:,K6-?:A!E,Z6}-?:A!E,$G6-?:<,)6.NUMBER CORRECT = =67B:,,.=:8<,,G AM6-?:<@,/6.NUMBER IN}CORRECT = C67B:,,.=:8<,,M AM6-?:<@,/6.NUMBER UNANSWERED = C67B:,,.=:8<,,M A6}-?:A R,$R" 6.G"67B:,%@,.=:,\2 "(?:A!Q:@0,26.C:6.DB6.EJ6.FG 6.M6.P6.R=6.ӠŠ}ҠϠG6.~SC6. W6-A!'6-A!0'6-A!B36-A!3?6-A!6K6-A!HW6-A!T}76-?:A!!,@%-6-?:A d,7 A D:GEOM.BASTXDSSCSKTMCPPMERWRSRRTSWCPXYKWelcome to the MATH MODULE of theHAYDEN SCORE IMPROVEMENT SYSTEM FORTHE SAT& one of three modules designedto help you rai}se your SAT scores.This Geometry Section is an effectivetool to begin your preparation for theMathematical section of the }ScholasticAptitude Tests.The system is easy tooperate so that you can concentrate onits content. All of the informationyo}u need to answer questions appearson the screen& as do instructions formoving from one part of the program toanother. More} detailed informationfollows in the User's Guide.~RAThis GEOMETRY SECTION providesinstruction and practice in solvingthe} entire range of geometry problemsof the types found on the SAT. Allfigures needed to solve the problemsare illustrated on} the screen.~RAThis section includes eleven parts inaddition to the User's Guide~` Complementary and Supplementary` A}ngles and Angle Sums` Parallel Lines` Angles of a Circle` Equalities of Angles and Sides` Pythagorean Theorem` Spe}cial Triangles` Perimeters` Areas` Similar Figures` Volumes` All Examples Without Tutormode~RAOther areas in the} Mathematicalsection of the SAT are Algebra& andQuantitative Comparisons and WordProblems; two separate sections withinth}is Math Module provide reviewmaterial in these areas.This section contains a two-sided diskwhich has a Program Disk side a}nd aReview Disk side. Always load theProgram Disk side first. Instructionson the screen will prompt you toinsert the ot}her side at theappropriate time.~RAMENUSThe MAIN MENU lets you move easilyfrom one section of the program toanother. S}imply press the keycorresponding to the letter next tothe section you wish to see.~RAThe first ten topics on the MAIN MEN}Ucombine two key aspects of the HaydenSystem~ DEFINITIONS& ANALYSIS ANDSTRATEGIES and EXAMPLES WITHTUTORMODE. First& DEFI}NITIONS providesthe background information you willneed to tackle the problem type on theSAT and demonstrates problem-solv}ingmethods& including valuable tricks andshortcuts.~RASecond& }TUTORMODE} gives you adetailed& step-by-step explanation }ofhow to arrive at the correct answer.By reviewing and practicing& youdevelop more efficient problem-solvingtechniques.~}RAThe ALL EXAMPLES WITHOUT TUTORMODEoption provides quick drill andpractice in all the problem typeslisted on the MAIN ME}NU so that youcan improve speed and accuracy. If youanswer incorrectly& you are shown thecorrect answer& but no detailede}xplanation is provided. At the end ofthe section& the computer tallies thenumber of questions answered correctlyand incorr}ectly& providing anindication of how well you havemastered the material.~RAWhen you make a selection from theMAIN MENU& }the System startspresenting the material or asks forthe other side of the disk to beloaded into the drive.~RAFUNCTION KE}YSA function key is a key which has aspecific effect on the program'soperation each time it is pressed.Whenever a menu }is on your screen thefollowing function keys areoperational~` M (Main Menu)` Q (Quit)Pressing }M} always brings }you back tothe MAIN MENU. Pressing }Q} causes thecomputer to ask if you really want toquit. If you answer }Y}& you end the}program. If you answer }N}& youcontinue where you left off.~RAWhile text is on the screen pressing}R} restarts the secti}on (erasing anyprevious answers that you may haveentered)& pressing }M} takes you tothe main menu and pressing }Q} enables}you to quit.~RAThe left-arrow key lets you pagebackwards through the text one screenat a time until the first screen of}the section is reached. When aquestion appears on the screen& yourprevious answer& if any& is shown. Youcan replace that a}nswer by enteringanother one& or you can leave youranswer undisturbed by pressing theleft-arrow again.~RAPressing the l}etter }O} leaves thecurrent question temporarilyunanswered and displays the nextquestion. At the end of the sectionyou ha}ve a chance to review all theunanswered questions.~ET~ETYSTEM FORTHE SAT& one of three modules designedto help you rai=The HAYDEN SCORE IMPROVEMENT SYSTEMFOR THE SAT is organized into threemodules. It includes both simulatedSAT exams and com}plete reviews of theareas typically covered by the Verbaland Mathematical sections of the SAT.In addition to this Math Mod}ule, thefollowing modules are available:~RAThe PRACTICE TESTS MODULE contains anAnalysis of the SAT, a Pre-Test, andtwo }Practice Tests.The ANALYSIS OF THE SAT gives youinsight into the workings of theactual exam -- its organization andscori}ng& plus test-taking strategiesand tips for raising your scores.~RAThe PRE-TEST is adiagnostic/prescriptive tool fordete}rmining your strengths andweaknesses in the areas typicallycovered by the SAT. It is a two-hourtest consisting of a mix of} Math andVerbal questions similar to that on anactual SAT. After you complete thetest your computer will provide scoresin} each of sixteen subjects whichcontribute to your Math and Verbalscores. This profile of yourperformance indicates which a}dditionalmodules in the Hayden System will beuseful in your preparation.~RAThe PRACTICE TESTS are two-hoursimulated exam}s with completeMathematical and Verbal sections timedand formatted to be representative ofthe latest SATs and scored on th}e SATscale. After reviewing your weakareas& take these Practice Tests andsee how your performance would measureup on the }actual exam.~RAThe VERBAL MODULE provides tutorials,drill and analysis in the Verbal areasnormally covered on the SAT.T}he VOCABULARY SECTION provides athorough review of antonyms& analogiesand sentence completions& as well asan on-screen dic}tionary with 1000words.~RAThe READING COMPREHENSION SECTIONoffers strategies and practice inresponding to questions abou}t thematerial just read. Working withpassages drawn from the mostup-to-date sources in a variety offields will help you i}mprove yourability to determine main ideas& torecognize logical implications and toextract factual information from whaty}ou read.~RAEach topic in a given section can beapproached in three ways~`acquiring background with`DEFINITIONS& ANALYSI}S AND STRATEGIES`gaining practice and instruction with`EXAMPLES WITH TUTORMODE`drilling with`EXAMPLES WITHOUT TUTORMODE}*NOTE~ This Geometry Section combinesDefinitions& Analysis and Strategiesand Examples With Tutormode.~ET~ETs and comt~SB~SH1127A D y B~SH0431C~SH0537E~SH0932k~SP189089210089210032210032~SP258040210089254089254089~SFB. Complement}ary and Supplementary` Angles and Angle Sums.Make sure you know thesetheorems& definitions andassumptions.1. Two} angles whose sumis a right angle arecomplementary.` }airs ofvertical angles and supplementaryangles.Vertical Angles` <1 = <3` <2 = <4` <5 = <7` <6 = <8Supplementar)?}y Angles<1+<2 = 180* <5+<6 = 180*<2+<3 = 180* <6+<7 = 180*<3+<4 = 180* <7+<8 = 180*<4+<1 = 180* <8+<5 = 180*~RA~Q)@}~SB~SP198028264028264028264028~SP198070264070264070264070~SP244012217082217082217082~SH0428A~SH0439B~SH0928C~SH0939D~)A}SH0236E~SH1133F~SH0533a~SH0834b~SH0336c~SH0535d~SH1031e~SF1. If G0 B?AUTORUN BAKBBAUTORUN SYSBGUGEOM BASB!AA BAB B.BBB BDBB B"FBB B3CBB BQEBB B'uDOS SYSBG1 B4GBB BJBB BKBB B) LCC B3HBB B"NIBB  = AC = BC~RCB5. (b) AB = BC Ans.Since Q  HH)1|}  hyhyB q L> Lm JJ  Ln*` dB%'1}}8  H H` 1 { LL   !L     Hh SY?  q  1L1~}  !? 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F0Ξ05: [ BDEHI1} VY8 B V  @  /DE `E:D1:DUP.SYSERROR-SAVING USER MEMORY ON DISKTYPE Y TO 1}STILL RUN DOS B;DE J V (` 9 V⪍ ઍ  -1}LLu DEHILV 9 .l 9 .l  `` s$B VBH1}I|DE V BLV nB,DE J V* \*` B V BLVDEHI BLVL1}1u H232435; 1 ;  hh@2 e1i1LHҍ 00) 08 109hh@ Ҡ2e1}1i1232435ޥ<<80}!"jINLINETRANSLATLOOFLSALDN(@#@6@@##265}-@6-@<;$,;,F((6.D:GBBD:HBBD:IBBD:JBBD:KBBD:LCCd;AU,;,@8@@25}R1:;NO TRANSLATE,,@6@@R1:-@$&@6.7<%&@,5} @@$$@@R1:"7,@@@R1:7START IO,5} @A6@@ @A-@@@@STOP IO05}4$$$$$$A D @N b$$@@R1:l7,@@@R1:5}7START IOv @A $$@@R1:7,@@@R1:75}START IO @A@STOP IO@  D:G1@R1:74\G. Special TrianglesMake sure you know these theorems&definitions and assumptions.~RA~SB~SP266095224095224031266095~S9}H1335s~SH0736h~SF`A. The 30*& 60*& 90* Triangle.1. The side(s) oppositethe 30* angle equalsone-half the hypotenuse (h)9}.` s = h/22. The side(s) oppositethe 60* angle equalsone-half the hypotenuse (h)` _times \/3.` h 9} _` s = - \/3` 2~RA~SB~SH1433s~SH0729s s~SH0934a~SP182095266095224031182095~SP224031224095224095224099}5~SF3. The altitude (a) ofan equilateral triangleequals one-half the` _side(s) times \/3.` s _9}` a = - \/3` 2~RA~SB~SH0733h s~SH1134s~SP210079258079258031210079~SF`B. The 45*& 45*& 90* Triangle1. T9}he side(s) opposite the45* angle equals one-half` _the hypotenuse (h) times \/2.` h _9}` s = - \/2` 22. The hypotenuse (h) _equals the side (s) times \/2.` _` h = s\/2~RA~SB~S9}H1134s~SH0730s d s~SH0434s~SP210079258079258031210079~SP258031210031210079210079~SF3. The side of a square(s)equal9}s half the diagonal (d)` _times \/2.` d _` s = - \/2` 24. The diagonal (d) of asquare equa9}ls the side(s)` _times \/2.` _` d = s \/2~RA~SD~Q1. Find the altitude of an equilateraltriangle 9}whose side is 10.` _ _(a) 5 (b) 5\/2 (c) 5\/3` _ _(d) 10\/2 (e) 10\/3~RCC` 9} _1. (c) 5\/3 Ans.Note~ Draw an altitude (a) to create a30*& 60*& 90* triangle.` 1 _` a = -10\/3` 9} 2` _` a = 5\/3 Ans.~RA~Q~SB~SH0729s s~SH09336~SH1326A s B~SH0333C~SP18209529}66095224024182095~SP224024224096224095224095~SF2. Find the side s ofequilateral triangle ABCwhose altitude is 6.` 9} _ _(a) 3 (b) 2\/3 (c) 3\/3` _ _(d) 4\/3 (e) 6\/3~RCD` _2. (d) 4\/3 Ans.Altitud9}e of an equilateral` S _triangle equals -\/3` 2` S _` -\/3 = 6` 2` _` S \/3 = 19}2` _` 3S = 12\/3` _` S = 4\/3 Ans.~RA~Q~SB~SH0330A~SH1329B~SH1029D C~SP2030242039}096238078203024~SP203078238078238078238020~SF3. In {ABC& AC = 8} and }0*~RA~SD~Q2. The distance around a rectangularswimming pool is 250 feet. The pool is50 feet wide. Find its length.(a)J?} 5' (b) 75' (c) 100' (d) 200'(e) 150'~RCB2. (b) 75' Ans.Let l = length of pool.` 50 + l + 50 + l = 250` J@} 100 + 2l = 250` 2l = 150` l = 75' Ans.~RA~Q3. Find the diameter of a quarter-milecircuJA}lar track. (use # = 22/7 andexpress your answer in yards)(a) 20 yds. (b) 40 yds. (c) 70 yds.(d) 140 yds. (e) 240 yds.~RJB}CD3. (d) 140 yds. Ans.Note~ 1/4 mile = 440 yds.` c = #d` 22` 440 = --d` JC} 7` 140 yds. = d Ans.~RA~Q4. Find the cost of framing a picture3 feet by 4 feet at $2.00 per foot.(a) $12JD}.00 (b) $14.00 (c) $24.00(d) $28.00 (e) $48.00~RCD4. (d) $28.00 Ans.Note~ Framing is perimeter.` p = 3 + 4JE} + 3 + 4` p = 14 ft.Cost = 14 x 2 = $28.00 Ans.~RA~Q5. Find the side of an equilateraltriangle whose perimetJF}er is equal tothat of a square of side 6}.(a) 4} (b) 8} (c) 12} (d) 24}(e) 9}~RCB5. (b) 8} Ans.Note~ The perimeteJG}r of the square is24}. Therefore the side of thetriangle = 24/3 = 8} Ans.~RA~Q6. The perimeter of an equilateraltriangJH}le equals the perimeter of asquare. A side of the triangle is b&and a side of the square is k. Expressb in terms of k.(aJI}) 3b/4 (b) 4b/3 (c) 3k/4(d) 4k/3 (e) 4b/3k~RCD6. (d) 4k/3 Ans.` 3b = perimeter of triangle` 4k = perimeter of squaJJ}re` 3b = 4k` b = 4k/3 Ans.~RA~Q~SB~SP224016189080252080224016~SP189080189128252128252080~SH062710}~SH063610}~SH1JK}3266}~SH13386}~SH102860* 60*~SF7. Find the perimeter of theaccompanying geometric figure.(a) 32} (b) 38} (c) 42}JL}(d) 44} (e) 52}~RCC7. (c) 42} Ans.The triangle is equilateralsince two angles are 60*.Therefore the common linein thJM}e triangle and therectangle is 10}& and thebase of the rectangle isalso 10}.10}+10}+6}+10}+6} = 42}~ET~ETn thHyI. AreasMake sure you know these theorems&definitions and assumptions.Area is the measure in square units ofthe surfacNO}e of an object.1. Triangle` Area = 1/2 bh2. Equilateral Triangle` 2` s _` Area = --\/3NP}` 4~RA3. Rectangle` Area = lw~RA~SB~SP217032255032231063189063~SP189063217032217063217063~SH0633h~SH0NQ}932b~SH1531h~SH1833b'~SH1333b~SP203104254104266135196135~SP196135203104203135203135~SF4. Parallelogram` Area = bhNR}5. Square` 2` Area = s6. Trapezoid` h` Area = -(b + b')` 2~RA~SD~SB~SC19207NS}1210056226071226071~SH0828r~SH0833r~SH0930n*~SH1133L~SF7. Circle` 2` Area = #r8. SectorA sector NT}is fraction ofthe area of the whole circle.` 2` Area = n/360 x #r` 2` n#r` NU} = ----` 360~RA~SD9. RingA ring is a figure with two concentriccircles (circles having the samecenter)NV}. To get the area of the ring -that is& the outer portion - subtractthe area of the smaller circle fromthe area of the larNW}ger circle.Area of Ring = Area of larger circle -Area of smaller circle.` 2 2Area of Ring = #R - #rNX}` 2 2Area of Ring = #(R - r )~RA10. Irregular Figures.To find the area of an irregularfigure~a. NY}Compute the areas of figures forwhich formulas exist.b. Determine their sum& difference& orfractional parts to obtain theNZ}required answer. In general~ Areashaded region = area outside - areainside.~RA~Q~SB~SP203024254024266055196055~SP1960N[}55203024203055203055~SH03338}~SH06314}~SH083310}~SP210085252085252128210128~SP210128210085210085210085~SH1430y~SFExamN\}ple~1. The area of a squareis equal to the area of atrapezoid with bases 8}and 10} and altitude 4}. Find a side of the N]}square.Area of square = Area oftrapezoid.~RA`2y = h/2 (b + b')`2y = 4/2 (8 + 10)`2y = 2 (18)`2y = 36y =N^} 6} Ans.~RA~SD~Q1. ABCD is a parallelogram& with AB =10}& AD = 6} and