12에이급1하 정답(001~009)-OK

Transcription

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2 p.12~ m n < =65= kg % % % cm % g % % ;2(; p.30~ =8y=5z= d e 32 b c 0 a f a=bc=de=f kg p.21~ % 227 2

3 4 =2y=10z=7 5 16%25% m=20.2 =83y= % =6y= m cm % p.52~ ceg cm 24 y= p.42~43 : 3 6ª5º:= % 4 3 p.62~ y 9 =37.5 y= cm 3

4 y= a=40 b=140 c=40 d=80 e=40 f= k n =90 y=45 =100 y=80 =60 y= ;1ª1;5 32;1 1; 5 16;1 1;5 38;1 1; 5 10;1!1);5 43;1 1; 5 27;1 1; =35 =42 =98 y=51 25 G= =100 =G // = =45 += = // =30 y=25 =25 y=35 z= ;1 1; p.73~ (a+b) p.84~85 4

5 SS b-c <a<b+c S 18 Q P R O cm p.91~ S YI PHXHPX 14 S 15 SS m 18 SS cm SS cm 2 p.106~113 1 SS 2 S 3 4cm 2 4 8cm 5 50cm cm cm cm p.99~ a> SS P P = P=PP=P ( ) P=P P P(S) P =P 17 G = =G =90 + =G G(SS) 5

6 cm cm 24 2acm cm 10 a+b+c cm cm cm 2 p.114~ pcm 2 P Q rcm 3 ;:!5@:^;cm 2 4 8cm =36 =108 p.134~ _(n-2) p.122~ pcm cm 2 p 135 3cm p ;2%;pcm ;; 4 ;;pcm {;; 3º;;p+24}cm pcm 2 6

7 y pcm ;; 2 ;;pcm 2 25cm 2 (25p-50)cm (2p+8)cm 50cm 2 {;; 2 ;;-;; 4 ;;p} cm 2 14 ;2%;pcm {50-;; 2 ;;p}cm 2 {;; 2 ;;p-25} cm 2 15 (200p-400)cm 2 50cm 2 8pcm 2 (50p-100)cm ap+8a8a 2-2a 2 p 17 {;; 9 ;;p+12} cm ;; 9 ;;pcm pcm 2 19 (16p-32)cm 2 12pcm {;; 2 ;;p-25} cm 2 {;; 2 ;;p+10} cm 20 (8p-25)cm 2 p.145~ =60 y= (12p-16)cm 2 (6p+8)cm 10 16pcm 40pcm pcm 2 (4p+24)cm (108-18p)cm 2 21 (4p+8)cm 2 (25p-50)cm a+2b p 3 23 (16p+216)m 2 24 ;:!3):);p cm 2 12pcm 2 25 pcm 2 26 (8p+12)cm ;3!; 30 (9p+14)cm (36p+56)cm ;3!; ;3@; ;3!; (6p+24)cm 13 (9p-12)cm 2 (16p-32)cm 2 7

8 1 {;; 4 ;;p+12}cm 2 2 6pcm 3 ;; 9º;;pcm 4 P p.156~ pcm 2 960cm pcm (50p+100)cm 2 r(a+2r)p 31 72cm cm 2 49pcm pcm cm 64cm 2 6cm p.173~182 p.164~ (n+1) V=;; 3 ;;pa 3 S=16pa 2 18 ;3*;cm 19 4cm pcm p pcm pcm pcm pcm 2 5 ;; 3 ;;cm pcm cm pcm cm pcm cm 3 ;; 3º;;pcm pcm 3 50cm cm 2 r(a+b)p 15 (12p+12)cm cm cm pcm pcm pcm 3 21 H G H G 8

9 H G 22 56pcm pcm pcm pcm 3 210pcm 2 14 ;:@3%:^;pcm pcm 2 50pcm pcm 2 17 (240-5p)cm 3 18 (36p+24) cm ;6%;a cm 2 48cm 3 27 ;; 5 ;; m (4p+84)cm2 28 ;; 5 ;;pcm pcm 3 30 ;2#; ;2!; ;2#; 4 {60-;2%;p} cm pcm 2 100pcm 3 4cm {1- }cm p p pcm ;2(;cm 2 15pcm 2 (24p-24)cm pcm 3 (58p+408)cm 2 p.183~ cm 3 360cm cm cm pcm 3 : ;3@; :pcm pcm pcm 3 6 : ;3@; :pcm 3 106pcm cm pcm : 3 :pcm 3 : ;9@; :pcm 3 28 ;:%3$:$;p 29 19cm 18cm cm pcm 3 360pcm pcm 2 400pcm 3 12 HHH H 1 (320p+640)cm pcm cm cm 2 p.194~195 9

10 m n < =65= kg ;2(; =8y=5z= p.12~ y 6 =42 2 +y= y

11 m n = 100_0.2= = = =13 _ 20 = 2_40+5_50+3_60 = 10 =51(kg) ;2#; <25+;2#; 23.5 < = ;2@;;1#;= ( )=14 (100_5+300_9+500_ _16+900_6) 50 = =536 [16~19] 40 ~ ~ ~ ~ ~ ~ = ;2(; 25 _;2!;

12 _0.58=116 =116-52=64 = =20 -=64-20= =48 ;5#; 48 ;5#;= =32- ={1.5_12+2.5_ _16+4.5_(32-) +5.5_} 80 = =282 =14 30 =40_0.2=8 y=40-( )=5 z=50-( )= p.21~ kg % % % cm % g % % [31~32] 40 ~ ~ ~ ~ ~ ~ kg 55kg 46kg 48kg48kg50kg50kg51kg 52kg54kg kg 4 46kg 26 12

13 10 5 = = 32 = = ( ) = ;4!0@;= = = =(7+19) 2=13 =(55+67) 2=61 5-=5_13-61= = =140 = =10 10 (40-12) 2=14 70 ;4!0$;_100=35(%) (14+2+8)= =26 12 =( = = ) 20 = = =20 20 ;2 0;_100=35(%) =100 ;1 0 0;= g 61g 40% 61g =60(%) 61g _100= a a=54 =

14 16 2 ~ 4 4 ~ 6 6 ~ 8 8 ~ ~ ~ ~ (3_26+5_18+7_10+9_4 +11_1+13_0+15_1) 60 =300 60= = a =17.75_(26+a) a= a a= = _0.1125=9 32g 56g 80-( )=38 ;8#0*;_100=47.5(%) ;6!0%;_100=25(%) = = = cm -10.1cm 6-(-10.1)=16.1(cm) =(7.5_4+12.5_8+17.5_a +22.5_ _4) (4+8+a+10+4)= g 56g 80_0.075=6 44g 50g 38-(8+7+6)=17 =(23_9+29_12+35_8 +41_7+47_17+53_6 +59_13+65_8) 80 = =44.075(g) _0.3=15 26 ( )_100=18(%) 27 14

15 28 50kg 55kg =0.28_600=168 =0.3_550= kg 65kg _0.16=96 550_0.1= _100=13.13?13.1(%) cm ( )_40= cm ( )_400= cm 80-14= % =2y=10z=7 5 16%25% m=20.2 =83y=78 p.30~ % =6y= m cm % d e 31 ;4!0$;= cm b c 180cm cm 1 160cm ( )_400= a f 0 a=b c=d e=f a+b+c 2 =21a+b+c=63 3 a+b+d =26a+b+d=

16 b+c+d =30b+c+d=90 3 a+c+d =28a+c+d= (a+b+c+d)=315 a+b+c+d=105 a=15b=21c=27d=42 6a+b+c-3d= = _100=55(%) (9+7+6)= =27 4 y=5 ;4 0;_2=;4 0;_ z=3+8 z= 2 +y+z=40-( ) = y=5z= =19 2 =2y=10z= % 480_;1 0 0;= = _100=16(%) _100=25(%) (4+8+6)= _;1 1;=10 ;4!0);= =(30_4+50_8+70_12+90_ _6) 40 =( ) 40 = = ( ) =10- ={45_2+55_4+65_+75_11 +85_13+95_(10-)} 40 = = =298030=210= =3 16

17 ;4 0;= ;4 0;= = = =24 =2+4+7=13 +=24+13= = =( ) 15 =480 15=32 =( ) 15 =495 15=33 15 ( ) 30=975 30= y 83 m=2n= ;2 0;=0.2 -y=5 >y y 80 =83y= ( )= = _100=40(%) 30 +y=9 3.8_30=

18 y = y=30 =6y= = _300= _50= _50= = m = = =13 ;5!0#;= =0.08_200=16 =0.12_300=36 =0.2_500= = =152 ; ;= _100=40 = ( )= _5= {3+5+;2^;}{;2^;+4+2}= m 40m 230m 35m 4 2+4=6 27 cm 140 ~ ~ ~ ~ ~ ~ 170 cm =_ =142.5_ _0.16 =+152.5_ _0.24 =+162.5_ _0.1 =156.4(cm) = =

19 155cm 160cm 155cm 160cm = =6 ;[^;_100=12 = (50-) ;2{;=(50-)-2 = =26 ;5@0^;_100=52(%) = =7 1+5= =;2 0;0.25=;4!;0.5=;2!;0.2=;5!; =50-( )= _100=85.7?86(%) kg 35kg 40kg =;2 0;=0.35 =;5!0$;=0.28 ={(17.5_1)+(22.5_3) +(27.5_2)+(32.5_4) +(37.5_7)+(42.5_2) +(47.5_0)+(52.5_1)} 20 =33.5(kg) ={(17.5_0)+(22.5_3) +(27.5_9)+(32.5_17) +(37.5_14)+(42.5_5) +(47.5_2)+(52.5_0)} 50 =34(kg) < 2 45kg 50kg 01 19

20 01 14 =7(12+a) p.42~ % (a+4)-7(12+a) 1 : 3 6ª5º:=6 =15_4-1_8-3_4 a= _ =;6$0$;_100= (%) (60-16) 2=22 2 7_20+9_20+7_20-( ) = = = =38 3 a b c d e(a+b c+d d+e) a+b+10=22 a=5b=7 e=14 c+d+14=38 c=11d= a b c d e(a+b b+c a 4 =9(a+4) d+e) a+b+c=22 a=5b=8c=9 e=15 a=6b=7c=9e=14 10+d+e=38 d<e d=13e=15 20

21 ab101010cd a+b+10=22 a=5b=7 d=14 a=6b=6d=13 10+c+d=38 c d c=14d= p.52~ ceg cm 24 y= l m n m//n m n 3 4 l P m Q n m//n m n 02 21

22 5 lmn lm lm 180 lm l ÍÍ Í G H 6 G G _30 +43_0.5 = _6 =258 = = _5-5.5 _43 = = = _7-5.5 _

23 = = ÍÍÍÍÍÍ _3 =6 2 4_3= = _3-5.5 _50.2 = = = a c egc e cm 7cm M 5 cm 7 cm N 2 2 =5cm M M =;2%;(cm) =12-5=7(cm) N N =;2&;(cm) MN =;2%;+;2&;=6(cm) MN =M +N =;2!;( + ) MN=;2!; =6(cm) 24 // =G( ) // G=( ) = y= 25 l//m a+=180 b+y=180 3+= y+y=180 =45 y=100 +y= l m Q P l//m 2+2=180 +=90 P l P=PQ+QP =P+P =+=

24 27 l m l//m = = = l ml n m n 3_2=6 29 =90-30 =60 y= =150 +y= y= =150 z=180 -(+90 ) =180 -( )=30 2(+y+z)= =90-21 =69 =180 -( )=55 =180 -( )=54 32 =180 -( )=56 =180 -( )=50 =360 -( ) = p.62~ y 9 =37.5 y= cm y= a=40 b=140 c=40 d=80 e=40 f= kn =90 y=45 =100 y=80 =60 y= ;1ª1;5 32;1 1; 5 16;1 1;5 38;1 1; 5 10;1!1);5 43;1 1; 5 27;1 1; 1 l//m//n a c b c a=b=c= =55 a+b+c=55 _3=165 24

25 6_5=30 2 l y m z l y=180 -+z +y-z=180 2(+y-z)=360 2 l 3 m =180 =30 l m n = = =( )+( ) = = G G // G= // G=64 = = =113 7 O=O=y O=2O=2y O=+y 3(+y=180 +y=60 O=60 8 // =H HG =G+y G=-y 9 2=75 =37.5 y= = =52 =

26 11 G==41 =G= = =180 = (180-2)=120 =60 13 MN =M +N =;2!; +;2!; MN=;2!; +;2!;_3 MN=2 =40(cm) =20(cm) =66 ac l ac u = =70 l m y =y y= GHIJ 2 H I J GH HI IJ J 7 G H I J y= =75 21 // PQ=PQ XPQ=PQY PX //QY 17 H G G H G H 4 4 l m = = =95 y=55 2+3y= =355 =y +y= G G==2_60 =120 = =60 =;2!;=30 26

27 24 p//q a=40 l//m b= =140 c= e+80 =180 e=40 d= e=80 f=d+60 = k n l m n 27 =60 y=60 +=120 +y=180 2a+2b=180 a+b=90 =90-30 =60 l m y 60 a =60-42 =18 b y=135 _;3!;=45 +y=180 =180 _;9%;=100 y=180 _;9$;=80 2y=3 y=;2#; ;2#;=30 + =60 y=;2#;=90 l y m = =145 z=125 y=180 -( )=90 +y+z= P//aQ//a P//Q P Q P Q a a P Q PRQR P//Q P Q P P R R Q Q 28 +y=135 =135 _;3@;=90 31 =65-45 =20 y= =

28 32 +y=155 +y= =68 2a 4a 4a b 2a 3a 2a+3a+4a=360 a=40 b=180-4a=20 a+b= _-6 _=60 =:ª5º5º:=16;1 1; 5 16;1 1; _-( _)= _5+0.5 _-6 _=30 =: ;5@5);º:=21;1ª1; 5 21;1ª1; _-( _)=30 =: ;5*5);º:=32;1 1; 5 32;1 1; =: ;5!5);º:=38;1 1; 5 38;1 1; _-6 _=90 =: 5º5º:=10;1!1); 5 10;1!1); _-( _)=90 =: ;5$5);º:=43;1 1; 5 43;1 1; 28

29 _-6 _=0 =: ;5%5);º:=27;1 1; 5 27;1 1; l m =60 = =110 l p.73~83 m 53 =180 -( )= (a+b) = =30 y=25 =25 y=35 z= ;1 1; = = = l a a b m b +=180 -(a+b) c d a b =180 =

30 l y m =y +y=240 3=180 =60 11 = =120 y= =130 +y=250 7 (+z)+(z+y)=180 +y+2z= z=180 z= L N L LK N NK 6 l m (M, I) (, H) =180 =50 N (G) L(J) K a= =50 b= =120 c= =110 g+f+e+d=360 a+b+c+d+e+f+g = = a+b=70 =2(a+b)= PQR= =60 SQR=;3!;PQR=20 15 a a 70 b b l l m m 24 =2=48 =180 -( )= = a= =120 =b=d c=60 30

31 a+b+c+d=120 _3+60 = =80 =80-45 =35 =+ =2(+)=160 += = b a a=90-27 _2=36 == =63 b= _2=54 2a+b=126 a+b=90 b=90-36 =54 2a+b=126 l m = = l m 25 = = = =20 l m =180 -( )=78 l 30 m = =75 65 I H G 100 I= =65 H // =65 ( ) I==65 ( ) I= =50 //G IG=100 ( ) H // I=100 ( ) =I-I = =50 l m =70 -( )=

32 42 += =42 82 l m y = =98 y=82-31 =51 25 G= =100 =G // = =45 += = // 28 =z= =60 y= y+z=60 _2+105 =225 l m 180 a+b+c+d+e+f+g =180 m 40 l y a b c d a+b+c+d+e e a+b+c+d+e+f f a g a+b a+b+c a+b+c+d y l m = =78 l m =55 =30 27 =55-25 =30 y=25 2=50 =25 2y=70 y=35 z=180 -( )=120 +y= =220 = =150 y= =70 +y= = _7-5.5 =126 30_7-5.5=126 =: 1 1 :=15;1 1; 30_7-5.5=-126 =

33 7 15;1 1; ' " p.84~85 30 '=( ) '=( ) 2=105 G= =75 HG'=GH=21 ( ) 60 G I 69 y H 69 J ' G=180 -( )=78 G =180 -( )=27 HG='HG=90-21 =69 ( ) y=180 -( )=42 +y= = I 'G+G''=''=90 'G=70 G H 70 ' ' l 20 m y G='G=70 +G=90 =I=20 ( ) I='=20 ( ' //' ) I=G'( ) ;2!;=y ;2!;+y= I= =80 2 =180 -( )=30 +2y=

34 G I K IK J KJ GK G _3-5.5 =76 =2;1 1; 30;1 1; ;1 1; 3 2;1 1; 5 2;1 1; 6 2;1 1; y 30_5-5.5y =158 y=-1;1 1; 56 6 y 30_6-5.5y =158 y=4 61;1 1; p.91~ SS b-c <a<b+c S cm =8 3+3=6 5+6=11<12 3+4=7>5 2+3=5>

35 4 7<3+5<9 (357) 9<3+7<12 (379) 9<5+7=12 (579) 5+9>12 (5912) 7+9>12 (7912) 5 = ( ) = ( ) ==90 = ( SS ) cm 6cm 3cm 4cm 7 = = = = 11 S SS 12 b-c <a<b+c 14 XOY O O' O ' 15 P O OPOP O =O ( ) P =P OP OP OP(SSS) 03 35

36 OP=OP OP O Q P R O O O O PQ PQ O O O O O O QR QR O O O = = (S) = 21 = =4cm ==60 = =6cm (SS) = =5cm 22 NM = ( ) N =M N M(SS) N=M=18 PN= =108 = = ==60 = = (SS ) = =60-36

37 =+ =60 -+ ( =) =60 =180 - = = m 18 SS cm SS cm a+(a+2)>a+6 a>4 P Q PQ = P =Q P=Q P Q(SS) P=Q=a =108 -a+a=108 5 O O O O O 6 P 03 p.99~ a> SS S YI PHXHPX 14 S 15 SS M Q MP MPMQ MQ P =P P P 90 P MP +MQ MPMQ

38 = = = = ===60 (SS) = = =60 = = = = = (SS) 8 O XYÍ P OP OP XOY 9 P Q O R PO PO(SS) O =O QO QO(SS) O =O O =O =O 10 P l Q Q PQÍ l P Q PQÍ PÍ PÍl m P =P =Q =Q = P=Q 11 ==180 2=90 = = (S) = = S 12 O =O =OP =OQ =Q =P OQPO 38

39 OQ=60 = (SS) 13 Y P H G X Q I P Y HI PHXYIQ PH = = = YI PHX =YIQ=90 PG=YPG=Y HPX =IYQ PHX YIQ(S) PX =QY 16 = = = =60 += (SS) = = 17 ==90 = =400m ==60 14 (S) = K M H HMKM M =M HM=KM MH=MK( ) MH=MK HM KM S H =K m G H = = =+60 = (SS) =+ = =60 +( )

40 =135 =75 = = = =90 =( ) 2=45 =- =75-45 =30 = =6cm =90 =;2!;_6_6=18(cm 2 ) 19 = = (SS) == == =180 4=120 =30 =30 =120 =30 P= =90 P = = =+ =60 + =+ = (SS) R P Q = = ==60 (SS) = P=P+P =+P ==60 Q=R=60 PQR 8cm 10 cm 4.5 cm 6cm G = =90 -= =90 -=90 - = (S) = =8cm 40

41 G=;2!;_(8+4.5)_6 G=37.5(cm 2 ) 03 p.106~113 P R(S) 3 HOIO OH=90 -HO=OI HO=IO=45 O =O HO IO(S) HOI=O 1 SS 2 S HOI=;4!;_4_4=4(cm 2 ) 3 4cm 2 4 8cm 5 50cm cm cm cm cm cm 24 2acm 4 G H 3cm 11 cm G ==90 -G =G = 1 G = ( ) G==90 =90 -=G G(S) G = =11-3=8(cm) G = ( ) G (SS) 5 2 P Q R PR = ==60 P=60 -PR=R = ==90 = (S = 03 41

42 = ==45 ==45 = = = =10cm = =10cm =;2!;_10_10=50(cm 2 ) 6 = = =240 - =60 + = =( // ) =240 - = = = (SS) =+ =+= = = + = + = = =( ) 2= = = = ==60 (SS) ==83-60 =23 M M MM M=M( ) M =M M=M( // ) M M(S) M+M =M=M( M =M ) =23(cm 2 ) 61 = = =60 -= (SS) =a =ba+b=119 =360 -(++) =360 -(+60 +) =360 -(60 +b+60 +a) 42

43 =360 -( )= J K L I G =G = 30 // ==30 =90 -G =90 -L=G G(S) = G H ==45 GH=-4 (SS) =90-30 =60 11 ==27 =90-27 _2=36 13 =20_20-4_80 =80(cm 2 ) P = ==90 =90 - =90 -( ) = (S) =8cm =6+10=16(cm) ;2!;_8_16=64(cm 2 ) = = =+60 = (SS) = +P=+ 12 L H I G K J JK = J=K=90 J =K 14 P==60 G 45 a 60 b J K(SS) G G 03 43

44 G =G 16 Q P G=G+ =+ =90 -=45 G= a=45 -(90-60 )=15 G(SS) =180 -( )=60 b=90-60 =30 PP = P=P P=P( ) P=P P P(S) P =P a+b= a ' a a P G 2a ' G = =G =a =90 +=G ='=90 -a G(SS) '=180-2(90 -a)=2a + '=180 -(90 +2a) =G+P =90-2a +90 '' =G+(180 -P) '='=90-2a =G ' =' -'' = -'' 90 =180 -P = -' =' P=90 '='=90 ' '(S) P '='=' 90 +(P+P)+P '='' =360 =2' P+P ' =(90 -P) 2 =+(90 +P) 44

45 =180 ( P=P) P=90 =60 + P=180 -P=90 =60 +( _2) = =86 a a a 2a 2a ==a ==2a ==2a =2a-a=a 5a=180 a=36 ( = ==a = SS) =a=36 =( ) 2=72 =+= =( ) 2=47 =- =60-47 = = =90 -= = G (SS) ==90-65 =25 =180 -( )=120 G= =30 19 ( = = =60 += SS) = +60 =+G G=60 26 G 77 H 21 P G G = G G = G=90 -G= G (SS) G 03 45

46 23 =;2!;_14_14=98(cm 2 ) PG=G( ) 10 cm 11 cm G= (G ) 60 P PG=90 - P P =90 -G=G P=G=90 P = ( ) P P = ( P ) P+P=180 P=60 -P= ( G=) P (SS) P+=180 P +P = +P =P P=P =P =11(cm) 22 =180 -=90 I H 60 G G GH =H ( ) G = ( ) G=+90 =H G H(SS) H=G=18 =180 -( )=35 H=35-18 =17 = =140 GG = =G=60 =G=90 =G=30 G(S) G = = G G==90 G = G= G= G (S) 46

47 = =acm 2 =a+a=2a(cm) P Q P P 03 p.114~ cm 2 3 ;:!5@:^;cm 2 4 8cm Q Q Q 1 P M N 3 L L LMN M MN ML MLN NL MNML MN =ML =;2!;_8=4(cm) NM=M-NM =NML-NM =LM M =M =5cm MN ML(SS) = L +L =4+1.5=5.5(cm) = ( ) = ( ) =- =-= (SS) =+ =+ =- M=;2!;_36=18(cm 2 ) 03 47

48 4 M =32 =18_;5#;=: 5 : =36-: 5 :=;:!5@:^;(cm 2 ) cm = == = = = = 180 -( ) = =10 2 =60-10 =50 ==50 = ( ) ==100 (S) = =8(cm) 04 p.122~ _(n-2) pcm cm p cm 2p cm 10 a+b+c cm cm pcm rcm 1 6_(6-3) = _(10-2) = n n (n-3) 48

49 a-b=n-(n-3)=3 3 n 180 _(n-2)=1080 n=8 8_(8-3) = = _;1 2;= _;1 2;= _;1 2;= a=0b=3 a+b=0+3=3 180_(7-2)= = =12 9_(9-3) = _(12-2) = p_5_;36{0;=4p = p_8_;36{0;=14p = p_8 2 _;3#6!0%;=56p(cm 2 ) ;2!;_8_14p=56p(cm 2 ) 240 2p_6_;36{0;=8 = p ;2!;_6_8=24(cm 2 ) p_8 2 _;36{0;=12 = 2p_8_ P O 135 2p 360=3(cm) 135 2p 240 p 135 2p OPOP OP=OP OP=OP 180 P 2PO+2OP=180 P=PO+OP=

50 PO=PO=OP=60 OP=OP=30 PO P =OP P +P OP=OP=30 PO= = P P=+b P=+c =P+P =++b+c =a+b+c ( +=a) 11 n =180 _;9@;= =+90 = cm O 30 //O O=O=30 O =O O=30 O= =120 μ 20= μ =5(cm) n =40 n=9 c a b a+d d 9_(9-3) 2 =27 a+b+c+d (180 ) 10 a b c P =360 50

51 15 =85 e a f d b g c a+c=fb+e=g a+b+c+d+e =f+g+d= =60 +2 =30 + =+ +=30 + =30 = = (+132 )=180 = = _(5-2)=540 a b cde a=540 _;3 0;=72 b=540 _;3 0;= c=540 _;3 0;=108 d=540 _;3 0;=126 e=540 _;3 0;=144 ==+=2 2+=120 =40 19 ( )_2=180 =20 18 n 180 _(n-2)=1260 n= = =18 +5= =2a=2b 2a+2b =360 a+b=70 = = μμ=oo=21 O=2O O 04 51

52 O=O=;2!;O O O=O=26 +;2!;O +=O+O 26 +;2!;O+26 =;2!;O+2O O=26 O= = P=aOP P =O =O OP=a OP O=a+a=2a O O=O=2a OP O=a+2a=3a μμ=oo μ24=a3a μ=8(cm) 23 =180 -( )=74 =a=b ==a( ) ==b( ) 74 +a+b=180 a+b=106 +=360-2_106 = O=( ) 2=30 O // O=O=30 OO=41 O28=14 O =7(cm 2 ) 25 =+2 y=+2 2+2= =110 +=55 +y=3+3 =3_55 = = _2=36 =360 -( )= y z _(5-2) =108 5 =z=( ) 2=36 y= _2=36 2-(y+z)=0 z = = =110 =540 -( ) =100 52

53 29 // =46 O O=180 -( )=97 30 p_3 2 _;2!;-p_1 2 _;2!; =4p(cm 2 ) ( )=2a+2b a+b=85 =180 -(a+b)=95 a a (180-2a)+(180-2b) =360 -( ) 2a+2b=206 a+b=103 =180 -(a+b)=77 a 105 a b b a a a b b b b 50 2a+2b =360 a+b=102.5 =180 -(a+50 +b) = a a b b a+b= =106 =180 -{360 -(a+b) =-( )} =30 34 PQRST _180 = r 2r 2r 6r =4r+2r+6r+2r =14r(cm) =2pr(cm) (2pr+14r)cm 2r 2r 2r 2r 2r 2r =2r_6=12r(cm) =2pr(cm) (2pr+12r)cm 04 53

54 1 2rcm P 04 p.134~ = = = =45 =45 = = =36 = ;2%;pcm ;; 4 ;;pcm {;; 3º;;p+24}cm pcm y pcm ;; 2 ;;pcm 2 25cm 2 2 =- =;2!;-;2!; =;2!;(-) =;2!;=;2!;_45 = == =36 2 =36 = _2=108 (25p-50)cm (2p+8)cm 3 O=360 _;8!;=45 O=360 _;8#;=135 54

55 μ =3μ O=3O=135 OH=;2#;O = =100 I+I=100 2=50 =180 -(I+I)=130 =180 -;2!;(+) =180 -;2!;(180 -) =;2!;+90 =;2!;_ = = =30 = =90 =360 -( )=130 = = P+2P=180 9 P+P=65 P=180 -(P+P) =115 P P+P=360 P+P= = = =180 =68 10 μμ=o75 23=O75 O=50 O=2O=2_50 =100 O=O+O O= =150 6 =+=60 =+=60 = = = μ=2μ μ=3μ O=3O= p_6_ =;2%;p(cm) 360 p_ _ =: 4 :p(cm 2 ) =2p_6_ =;; 3º;;p(cm) 04 55

56 100 =2p_12_ =;; 3º;;p(cm) 360 ;; 3º;;p;; 3º;;p=12 2 =p_ _ =10p(cm 2 ) 360 =p_ _ =40p(cm 2 ) p40p=14 4 : 3º:p+12_2=: 3º:p+24(cm) r =2pr_;36{0; r 612=12 k 2 =pr 2 _;36{0; = = // ==60 = = =( ) 2=50 =60-50 =10 =+=40 =90-40 =50 14 a 2a a a O O=a //O O=O=a O =O O=O=a O O=O+O=2a μ =2 μ+μ =9-(+2)=6 r =14 k 4 12 P=97-57 = P = =72 56

57 16 = =12 = = = =60 =360 -( )=96 a c d a+b=c+d 180 _(5-2)= p_ _ -p_ _ =18p(cm 2 ) 18 a=180 -( )=20 b=180 -( )=60 c=180 -( )=70 a+b+c= =a =(180 -a) 2 =90 -;2!;a b 2a+2b=360 -( )=230 a+b=115 =180 -(a+b) = =65 21 // = =65 // ==65 G G= =140 = =51 22 O= =130 O= =110 O= =120 μμ μ =OOO = = = =150 =( ) 2=15 (SS) z=60-15 _2=30 y= =105 +y+z=150 ==+y 180 =+(+y)+90 -;2!;a 24 a 6cm 6cm b 4cm a=4+2y =a=b a =p_6 2 _;2!;-p_3 2 _;2!; 04 57

58 =18p-4.5p=13.5p(cm 2 ) b =p_5 2 _;2!;-p_2 2 _;2!; =12.5p-2p=10.5p(cm 2 ) =a +b =13.5p+10.5p=24p(cm 2 ) 25 = = ==36 ==36 I I=I=36 = =72 (SS ) G=G= =72 G JGHGIH JI(SS) J =G =GH =HI =IJ GHIJ a 2a 2a 90 -a 2a O 2a T O 2a O=O=O=O =OT=2a O =O O=(180-2a) 2=90 -a OT=90 TO 90 -a a=360 9a=135 a=15 OT=10a=150 = = = =+ = =30 == =45 = _2=90 == =60 60 ==2 ==+ =3 ==+ =4 X=180-4 =90 =G G =4 +4=90 =18 28 =a=b 58

59 a+b++134 =360 a+b+=226 2a+2b =540 2a+2b+=340 - a+b=114 = =112 = =( ) 2=75.5 = =( ) 2 =30.5 = =45 == =-30 =;2!;(180 -) ;2!;(180 -)+2(-30 )=180 = p_10 2 _;4!;-p_5 2 _;2!; =: 2 :p(cm 2 ) a b 10 cm a b ;4!; 10_10_;4!;=25(cm 2 ) p_5 2 -;2!;_10_10 =25p-50(cm 2 ) 30 S 1 =p_2 2 -p_{;2#;} 2 -p_{;2!;} 2 =;2#;p S 2 =p_{;2!;} 2 =;4!;p S 1 S 2 =;2#;p;4!;p=61 31 =a=b +b=a+56 =56 +(a-b) a+56 +(180-2b) =360 2a-2b=4 a-b=2 =56 +2 =58 a a b b =a=b + = a-b= a+b=34 + = a-b=50 = =130 =96 +a+b a+b=96-62 =34 = =

60 32 =a=b 60 +2a=52 +2b b-a=4 60 +a=+b =60 +(a-b)=60-4 = == =+6 =+6 =( ) 2=93 =93 33 OO' 2cm O 4cm O' 2cm 4cm O' =4_4+2p_1=2p+16(cm) O =2_4=8(cm) (2p+16)-8=2p+8(cm) =60 y= (12p-16)cm 2 (6p+8)cm 40pcm pcm 12 24pcm 2 (4p+24)cm (108-18p)cm 2 (6p+24)cm 13 (9p-12)cm 2 (16p-32)cm 2 50cm 2 {;; 2 ;;-;; 4 ;;p}cm 2 14 ;2%;pcm {50-;; 2 ;;p}cm 2 {;; 2 ;;p-25}cm 2 15 (200p-400)cm 2 50cm 2 8pcm 2 (50p-100)cm ap+8a 8a 2-2a 2 p 17 {;; 9 ;;p+12}cm ;; 9 ;;pcm pcm 2 19 (16p-32)cm 2 12pcm {;; 2 ;;p-25}cm 2 {;; 2 ;;p+10}cm 20 (8p-25)cm 2 21 (4p+8)cm 2 (25p-50)cm 2 4a+2b 22 p 23 (16p+216)m 3 2 p.145~155 60

61 24 ;:!3):);pcm 2 12pcm 2 25 pcm 2 26 (8p+12)cm ;3!; 30 (9p+14)cm (36p+56)cm ;3!; ;3@; ;3!; P+P ={360 -( )} 2=73 P=360 -( )=139 = =41 = =124 =124 2=62 = =118 2 =a=b 2a+2b=180 a+b=90 =2b a+2b=b+ =a+b=90 3 PQ ;2!; +y=720 -( ) =180 4 =P =P P P P=P=90 -P =90-60 =30 P=P =( ) 2=75 a= =150 5 OI+OI=180 OI y=360 -( )=120 O+O= =60 = _2=60 6 // =='=50 = _2= _7-360 _2=540 H G K X Y I J Z X X 180 +=X+X YJK IZY 360 +K+J 04 61

62 =YIZ+Z+YZ IZGH P=+P+P = = _(7-2)=900 c a b f e h g d a+b=c+d e+f=g+h =900 9 p_4 2 _;4!; +2{p_4 2 _;4!;-;2!;_4_4} =4p+2(4p-8) =12p-16(cm 2 ) p_4 2 4 _;4!;+ 2 (p-2) 2 =4p+8p-16 =12p-16(cm 2 ) 4+4+{2p_4_;4!;}_3 =6p+8(cm) f g c e 10 2p_8_;2!;+2p_5_;2!;+2p_3_;2!; d =16p(cm) p_8 2 _;2!;+p_5 2 _;2!;-p_3 2 _;2!; a+b a b =40p(cm 2 ) g=a+b e=f, c=d+e=d+f = = += =80 P+P =;2!;(+)=40 =110 -( )=28 =+64 =92 = =52 =180 -(+) =180 -( )=36 62

63 12 =60 =p_ _ =24p(cm 2 ) 360 =12_2+2p_12_ =4p+24(cm) =12_12-{p_6 2 _;2!;+6_6} =108-18p(cm 2 ) =12_2+2p_6_;2!; =6p+24(cm) 13 (10+2) 2=6(cm) p_ _ -;2!;_4_6 360 =9p-12(cm 2 ) p_4 2 -;2!;_8_8=16p-32(cm 2 ) H H(SSS) H=90 = H 10 cm 10 cm =;2!;_10_10 =50(cm 2 ) 10 cm = =+ =+ ={5_5-p_5 2 _;4!;}+;2!;_5_5 =: 2 :-: 4 :p(cm 2 ) p_10_ =;2%;p(cm) ;2!;_10_10-p_10 2 _ =50-: 2 :p(cm 2 ) p_10 2 _;8!;-;4!;_10_10 =: 2 :p-25(cm 2 ) 20 cm 8 _ ={p_10 2 _;4!;-;2!;_10_10}_8 =200p-400(cm 2 ) 10 cm 20 cm (p-2)_4=200p-400(cm 2 ) 10 cm ;2!;_10_10=50(cm 2 ) p_4 2-2_p_2 2 =8p(cm 2 ) 04 63

64 =19p(cm 2 ) 20 cm p_10 2 _;2!;-;2!;_20_10 =50p-100(cm 2 ) 4a a a =4a_2+2p_a =2ap+8a =4a_2a-2_p_a 2 =8a 2-2a 2 p = = = =p_8 2 _;4!;-;2!;_8_8 =16p-32(cm 2 ) =2p_8_;4!;+2p_4 =12p(cm) _2+2p_6_ p_4_ 360 =: 9 :p+12(cm) {p_ _ -p_ _ } p_ _ 360 =: 9 :p(cm 2 ) 45 =p_10 2 _;8!;-;2!;_5_10 =: 2 :p-25(cm 2 ) =2p_5_;2!;+2p_10_;8!;+10 =: 2 :p+10(cm) cm 6cm 20 8cm S S S G H 2cm GHG 8cm ;8!; 10cm =p_10 2 _;4!;-p_6 2 _;6!; ;4!;S 1 -S 2 64

65 21 S 1 -S 2 =p_8 2 _;8!;-10_10_;4!; S 1 -S 2 =8p-25(cm 2 ) 4cm 12 cm 8cm M 5 5 4m 54m 54_4=216(m 2 ) 5 4m 16pm 2 (16p+216)m 2 {8_4+p_4 2 _;4!;}-;2!;_4_12 =4p+8(cm 2 ) {p_ _ -;4!;_10_10}_2 360 =25p-50(cm 2 ) 22 b 2a b a a l 23 8cm 60 =2p_a =+2p_b =+2p_2a_ 360 4a+2b = p ' ' - =( =) =p_ _ =;:!3):);p(cm 2 ) 360 =p_ _ =12p(cm 2 ) 360 = 6cm 6cm O O' 6cm 120 1cm1cm + =p_ _ -p_ _ =p(cm 2 ) p_2_;3!;+2p_4_;3!; 04 65

66 +2p_6_;3!;+2_3+6=8p+12(cm) I=90 +;2!;= c b a i P=cQ=d 2a+2c=180 h d g e f a+b++i 9 2 2b+2d=180 IP=IP=90 P=180 -I=55 QP QP+QP+Q=180 Q=180 -( )= _9-360 _2=900 Q=;2!;=35 k j p n o m y l m+n=+y 29 H j+k++p 180 _(5-2)=540 =- = =360 O G O O O G OOG O =O μ=μ O=O 28 c a a c 70 I b d b d d Q O=OG=90 O=OG O OG(S) O =OG =G O =ro =a =b P O=O=O I=aI=b 70 +2a+2b=180 a+b=55 I=180 -(a+b)=125 O=;3!;_90 =30 =pr 2 _ ;2!;ab 66

67 =-{pr 2 _ =;1 2;pr O -;2!;ab} =pr 2 90 _ =;4!;pr O ;1 2; ;4!;=;3!; +(p_9 2 -p_5 2 )_;2!; =36p+56(cm 2 ) O 4_(9p+14)=36p+56(cm 2 ) OG OG O(SSS) O=OG=O H=O-OH =O-OH =OH O O =OO=30 90 =13 31 a a a G =a=b P=c 3a+3b+117 =180 a+b=;3!;( )=21 = =159 P=P-P P=;3@;(-) P=;3@;_=;3@;_117 P H Q b b cc b c S R 30 2cm O G P=78 S=S-S 8cm 6cm 10 cm H I S=;3!;(-) S=;3!;_=;3!;_117 ' 2p_7_;2!;+2p_2_;2!;+8+6 =9p+14(cm) 4_(8+6)+p_4 2 _;2!; S=39 PQSR 360 PQS+SRP =360 -(RPQ+RSQ) =P+S= =

68 GH= _2=138 G+GH =360 -( )=63 =180 -;3!;(+) =180 -;3!;(180 -) =120 +;3!; S=;3!; PQS+SRP =P+S= G+GH =360 -(G+) =360 -(180 +) =180 - O+O=180 O 90 p_ _ +p_ _ ;2!;_3_8 =: 4 :p+12(cm 2 ) 2 O l O ' O' ' 3cm 3cm O ' ' O =2p_3_;4!;_2+2p_3_;2!; =6p(cm) 04 3 P R 1 p.156~157 1 {;; 4 ;;p+12}cm 2 2 6pcm 3 ;; 9º;;pcm 4 P 5cm O 4cm k O 4cm 4cm 3cm () 3cm 5cm O OPQ=90 OP // Q R R R=PO=R =R =10cm R P O Q P 10 cm R S 68

69 P=20 RS=20 _2=40 P=70 RS=70 _2=140 R 2p_10_ J H G I k =: 9º:p(cm) J H G I O J K O=K O=K K ==36 = =J >K K P Q J K J I I k k O H O H G G I =I I=108 I=I=36 36 G GIH IJ (S) J GH IJH(SS) HJ HJ O P=5_ Q =5_O O 04 69

70 05 p.164~ (n+1) V=;; 3 ;;pa 3 S=16pa 2 18 ;3*;cm 19 4cm pcm p pcm pcm 2 960cm pcm (50p+100)cm 2 r(a+2r)p 31 72cm cm 2 49pcm 2 5 n 3n=27n=9 9+2= r ;3$;pr

71 p_6 2 _h=96p h=;3*; cm r cm n n+1=10n=9 =9+1=10y=2_9=18 +y=10+18= p_12_ =8p(cm) 360 rcm 2pr=8p r=4 8cm a 3cm a 2p_8_;360;=2p_ V=;3$;p_(2a) 3 =;; 3 ;;pa 3 S=4p_(2a) 2 =16pa 2 18 ;3!;_p_6 2 _8=96p(cm 3 ) hcm a= cm =;3$;p_6 3 =288p(cm 3 ) 2cm =;3$;p_2 3 =: 3 :p(cm 3 ) 288p: 3 :p=271 6cm 2cm

72 ab a 3 b 3 62= = p_3 2 +p_3_6 =9p+18p=27p(cm 2 ) 6cm 22 6p cm 3cm 23 rcm 4pr 2 =36p r=3( r>0) =p_3 2 _6=54p(cm 3 ) 24 2a 2a =;3$;pa 3 =(2a) 3 =8a 3 ;3$;pa 3 8a 3 6 =p6=1 p 6 p cm 6cm 4cm 8cm =;3!;_p_8 2 _6+p_8 2 _4 =384p(cm 3 ) 28 2p_6_;36{0;=2p_3 =180 =;2!;_p_6 2 +p_3 2 =27p(cm 2 ) ;2!;_(12+18)_8_2+10_15 +12_15+8_15+18_15 =960(cm 2 ) 12 cm 18 cm 8cm cm 8cm 12 cm 10 cm r cm 8cm rcm 150 2pr=2p_12_ r=5 360 =p_5 2 +p_5_12 =85p(cm 2 ) 15 cm 18 cm 10 cm 72

73 29 l =12_12_;2!;=72(cm 2 ) k 32 2_[;2!;_(4+5)_4 +;2!;_(4+7)_3+;2!;_7_1] 30 5cm 10 p cm cm = =76(cm 2 ) p_7 2 =49p(cm 2 ) 10 cm 05 p.173~182 {p_ _ }_2+(10_5)_ {2p_5_ }_ =50p+100(cm 2 ) + _;2!; =pr_a+4pr 2 _;2!; =par+2pr 2 =r(a+2r)p cm ' 3cm 2p_12_;36{0;=2p_3 = pcm cm 64cm 2 6cm 2 216pcm pcm pcm 2 5 ;; 3 ;;cm pcm cm pcm cm pcm cm 3 ;; 3º;;pcm pcm 3 50cm cm 2 r(a+b)p 15 (12p+12)cm cm cm pcm pcm pcm pcm pcm pcm ;; 5 ;;m 28 ;; 5 ;;pcm pcm 3 30 ;2#; ;2!; ;2#;

74 1 rcm 4pr 2 =144p r=6 =;3$;p_6 3 =288p(cm 3 ) 14= =18 cm 6 2 =96=6_4 2 =4 8_8=64(cm 2 ) h cm 4cm 5 ;3!;_{;2!;_4_4}_4=: 3 :(cm 3 ) 6 p_3 2 +p_3_5=24p(cm 2 ) 7 8_8+{;2!;_8_10}_4=224(cm 2 ) 8 3cm 8cm 9cm 5cm 9cm ;3!;_p_9 2 _3+p_9 2 _5=486p(cm 3 ) hcm 4cm p_4 2 _h=96p h=6 2 p_9 2 +p_9_15=216p(cm 2 ) 3 9 =;2!;_(9+12)_8+;2!;_12_3 =102(cm 2 ) =_ =102_5=510(cm 3 ) 10 6cm 15 cm + 8cm 24 cm =p_8 2 _24=1536p(cm 3 ) =;3!;_p_6 2 _15+;3$;p_6 3 _;2!; =324p(cm 3 ) 6cm 4 _;4#; + 6cm =4p_6 2 _;4#;+p_6 2 =108p+36p=144p(cm 2 ) 11 V =y 2 V = 2 y V V =y 2 2 y=y=21 2=y S =4y+2y 2 =4_2+2_(2) 2 74

75 = =16 2 S =4y+2 2 =4_2+2 2 = =10 2 S S = =85 12 ;3!;_4_4_9=48(cm 3 ) ;3!;_p_2 2 _6+;3!;_p_2 2 _4 5cm 4cm = + 6cm 3cm =;2!;_6_4+;2!;_p_3 2 +;2!;_p_3_5 =12p+12(cm 2 ) 16 20_12_16-16_8_14=2048(cm 3 ) =: 3º:p(cm 3 ) 17 6cm 4cm 13 8cm 6cm =;3!;_{;2!;_6_8}_4=32(cm 3 ) 2cm p_2 2 _6=24p(cm 3 ) 12 cm 5cm 5cm ;3!;_{;2!;_5_5}_12=50(cm 3 ) 14 7cm 8cm 10 cm (8_10+7_10+8_7)_2 =412(cm 2 ) p_r_a+p_r_b=r(a+b)p =10_10_10-32=968(cm 3 ) 18 12cm - 6cm ={;3$;p_12 3 }_;2!;-{;3$;p_6 3 }_;2!; =1008p(cm 3 ) 19 6cm + =4p_6 2 +2p_6_8=240p(cm 2 ) cm 6cm 20 cm 15 p_16 2 _20-p_6 2 _20=4400p(cm 3 ) 05 75

76 21 H G 25 p_5 2 _7-;3!;_p_5 2 _3=150p(cm 3 ) V H H G G V V 22 6cm 4cm 4cm _;2!;+ =4p_4 2 _;2!;+p_4_6=56p(cm 2 ) 23 lcm 2pl=2p_6_;3&;l=14 p_6 2 +p_6_14=120p(cm 2 ) 24 l 7cm 4cm 26 N N M P M P N N M P M P 27 ;2!;_(7+9)_3_10+15_2_10 =540(m 3 ) hm 15_10_h=540 h=: 5 : 5cm 76

77 28 ;3$;pr 3 2pr 3 =23 5cm H 3cm ;2#; 4cm H 5_H =4_3 H =: 5 :(cm) =;3!;_pr 2 _2r=;3@;pr 3 ;3$;pr 3 ;3@;pr 3 =21 ;2!; 5cm H 3cm 4cm ;3!; ;2#;_;3!;=;2!; =;3!;_p_{: 5 :} 2 _5 =: 5 :p(cm 3 ) V2 5cm 3cm 4cm V 1 =: 5 :p(cm 3 ) V 2 =;3!;_p_4 2 _3=16p(cm 3 ) V 1 V 2 =: 5 :p16p=35 29 =;3!;_p_6 2 _8-;3!;_p_3 2 _4 =84p(cm 3 ) 84p 6=14p(cm 3 ) 30 =pr 2 _2r=2pr 3 =;3$;pr 3 =pr 2 _2+2pr_2r=6pr 2 =4pr 2 4pr 2 6pr 2 =23 ;2#; =pr 2 pr 2 4pr 2 = pcm 3 (58p+408)cm 2 p.183~ pcm pcm 3 6 : ;3@; :pcm 3 106pcm cm pcm

78 10 672pcm 3 360pcm pcm 2 400pcm pcm 3 210pcm 2 14 ;:@3%:^;pcm 3 2 =p_ =204p(cm 3 ) pcm 2 50pcm pcm 2 17 (240-5p)cm 3 18 (36p+24)cm cm 12 cm 12 cm 2p cm ;6%;a cm 2 48cm 3 (4p+84)cm 2 {60-;2%;p}cm pcm 2 100pcm 3 4cm {1- }cm 3 p p 23 3pcm ;2(;cm 2 15pcm 2 (24p-24)cm cm 3 360cm cm cm pcm 3 : ;3@; :pcm 3 3 ={p_ _ }_2+(17_12)_ p_ =58p+408(cm 2 ) l 3cm 3cm (4p_3 2 )_;2!;+2p_3_6+p_3 2 =63p(cm 2 ) 6cm : 3 :pcm 3 : ;9@; :pcm 3 28 ;:%3$:$;p 29 19cm 4 18cm cm 3 a P Q O a 1 =;3!;_p_5 2 _6=50p(cm 3 ) = - =;3!;_p_10 2 _12-50p=350p(cm 3 ) =50p350p=17 V 1 =;3$;p_{;2;} 3 =;6!;pa 3 V 2 =;3$;pa 3 _;2!;-V 1 V 2 =;2!;pa 3 V 1 V 2 =;6!;pa 3 ;2!;pa 3 =13 78

79 5 3cm 8cm 6cm p_6 2 _8-;3!;_p_3 2 _8=264p(cm 3 ) 6 =p_5 2 _4+;3$;p_4 3 _;2!; =;:$3@:*;p(cm 3 ) l 9 a =a 3 =p_5 2 +2p_5_4+4p_4 2 _;2!; 10 PQR =;3!;_;2!;_;2;_;2;_;2;= 48 =a 3 - =;4$8&;a 3 48 a 3 ;4$8&;a 3 = cm a 3 8cm 8cm 6cm 12 cm a 3 +(p_5 2 -p_4 2 ) =106p(cm 2 ) 7 - =;3!;_50_50_50-;3!;_20_20_20 =39000(cm 3 ) 8 =4p_3 2 =36p(cm 2 ) =2p_3_6 =36p(cm 2 ) 36p36p=11 =;3$;p_3 3 =36p(cm 3 ) =;3!;_p_3 2 _6 =18p(cm 3 ) =p_3 2 _6 =54p(cm 3 ) 36p18p54p=213 p_3 2 _2+36p=54p(cm 2 ) ;3!;_p_12 2 _16-;3!;_p_6 2 _8 =672p(cm 3 ) p_12 2 +p_6 2 +(p_12_20 -p_6_10) =360p(cm 2 ) 11 =(p_6 2 -p_4 2 )_2+2p_6_20 +2p_4_20 =440p(cm 2 ) 10 cm 10 cm 12 cm 6cm =p_6 2 _20-p_4 2 _

80 =400p(cm 3 ) 12 H H H H HH H H 15 pr 2 _4r=256pr 3 =64 r=4 ;3$;p_4 3 =;:@3%:^;p(cm 3 ) l 5cm 3cm 13 l 13 cm 12 cm 2p_5_3=30p(cm 2 ) p_5 2 _3-;3!;_p_5 2 _3 =50p(cm 3 ) 5cm 16 l =p_5 2 _12-;3!;_p_5 2 _12 2cm =200p(cm 3 ) 13 cm 3cm 3cm 4cm 1cm 12 cm p_4 2 _2+2p_4_3+2p_3_2 =68p(cm 2 ) 5cm =p_5 2 +2p_5_12+p_5_13 =210p(cm 2 ) 14 rcm hcm 2prh=4pr 2 _2 h=4r 256pcm 3 17 ;2!;_(3+5)_3_20-p_{;2!;} 2 _20 =240-5p(cm 3 ) 18 P O P + O ={;3!;_p_4 2 _9}_;4#; 80

81 +;3!;_{;2!;_4_4}_9 =36p+24(cm 3 ) 19 (SS ) =60 a 3 -;3!;_{;2!;_a_a}_a=;6%;a 3 20 =(3_8)_2+(3_3)_2 +(1_2_9)_2 =102(cm 2 ) =(2_1_1)_24=48(cm 3 ) =(3_4)_2-p_1 2 _;2!;_2 +(3_5)_2+(4_5)+(2_5) +2p_1_;2!;_5 =4p+84(cm 2 ) =4_3_5-;2!;_p_1 2 _5 =60-;2%;p(cm 3 ) 21 2p_5_12=120p(cm 2 ) ;3!;_p_5 2 _12=100p(cm 3 ) hcm p_5 2 _h=100p h=4 ;3!; 12_;3!;=4(cm) ;2!; cm ;2!;_5_12 =;2!; 6+;2!;_(+5)_6 =;2%; ;2!; ;3!;_p_{;2%;} 2 _6=: 2 :p(cm 3 ) 100p : 2 :p=8 22 rcm 4 2pr=8 r= p hcm 4 16 h=8-2_2r=8-4_ =8- p p =pr 2 h 4 =p_{ } 2 16 _{8- } p p = {8- } p p = {1- }(cm 3 ) p p 23 μ =2p_6_;4!;=3p(cm) 3cm Q P O 6cm R QPRP PQ=PR=90 P 05 81

82 O O(SS) O=O QP RP(S) PQ =PR =;2!;_6=3(cm) QPR=90 PQR=;2!;_3_3=;2(;(cm 2 ) 6cm 10cm ;4!; =p_6_10_;4!;=15p(cm 2 ) = O - PO =;3!;_p_6 2 _8_;4!; -;3!;_;2!;_6_6_4 =24p-24(cm 3 ) 24 2cm 4cm cm 4cm 6cm ;2!;_6_8=;2!; 4+;2!;_(+6)_4 =3 =;3!;_12_12_8-;3!;_6_6_4 =336(cm 3 ) =;2!;_(6+12)_5_4+6_6+12_12 =360(cm 2 ) 25 (9_9-3_3)_6+3_3_4_6 =648(cm 2 ) 26 ;1ª6; rcm p_6 2 _;1ª6;=pr 2 r=;2(;( r>0) cm cm ;2!;_6_8=;2!;_;2(;_(8-) ;2!;_6_8=+;2!;_{;2(;+6}_ =2 ab a 2 b 2 rcm ;1ª6;={;4#;} 2 r=6_;4#;=;2(; 10 cm 6cm l 5cm12 cm cm (8-)cm cm 82

83 ;2!;_10_(12+) =;2!;_(5+10)_12+;2!;_5 =12 =;3!;_p_10 2 _24-;3!;_p_5 2 _12 =700p(cm 3 ) l l cm 3cm 4cm 2cm 3cm ;2!;_5_(4+) =;2!;_3+;2!;_(3+5)_4 3cm y cm 4cm cm 4cm (3-)cm (5-y)cm =6 =;3!;_p_5 2 _10-;3!;_p_3 2 _6 -p_3 2 _4 =;3!;_p_4 2 _y+;3!;_p_4 2 _ =: 3 :p(cm 3 ) +;3!;_p_4 2 _(3-) +;3!;_p_4 2 _(5-y) =;3!;_p_4 2 _(y y) =;3!;_p_4 2 _8 l 4cm y cm 2cm (6-)cm 6cm cm =: ;3@; :p(cm 3 ) l ;2!;_4_6+;2!;_2_ =;2!;_2_6+;2!;_4_(6-) =2 4cm 8cm ;2!;_4_6+;2!;_2_2 =;2!;_4_4+;2!;_2_2+;2!;_6_y y=;3$; =;3!;_p_4 2 _8=;:!3@:*;p(cm 3 ) =;3!;_p_4 2 _6+;3!;_p_2 2 _6 -;3!;_p_{;3$;} 2 _

84 =: :p(cm 3 ) S 8 P Q 2 O 2 2 O QP(S) P =O =2cm ={;3!;_p_8 2 _8-;3!;_p_2 2 _2} =+p_2 2 _4-;3!;_p_2 2 _2 =;:%3$:$;p ~ ª º { } =+ cm ;2!;_6_12 =;2!;_4_+;2!;_(4+6)_(12-) =8 =8cm =12-8=4(cm) =12+4=16(cm) { } 3cm 16+3=19(cm) ª º { } 12+6=18(cm) 18cm 30 QGHQPHR QHGR P S 84

85 PSQ R Q =P +R =4+4=8(cm) ={;3!;_8_8_8} =+[;3!;_;2!;_(4+10)_8_8] =+[;3!;_;2!;_(10+14)_8_8] =576(cm 3 ) O =O =8cm O ==45 O= =90 45 ;4!;_p_8 2 _20+;2!;_8_8_20 =320p+640(cm 3 ) 14 cm 8cm 4cm 2 10 cm 8cm 18cm 8_8_18_;2!;=576(cm 3 ) V V 25 cm 20 cm V 1 p_( )=72p(cm 2 ) 45-20=25(cm) ;2!; 05 V 2 72pcm 2 20cm p.194~195 ;2!;_72p_25+72p_20 1 (320p+640)cm pcm cm cm 2 1 O 8cm 45 3 =900p+1440p=2340p(cm 3 ) I J H G G I G J IJ 05 85

86 J H K G H G G JH G K JK =;3!;_{;2!;_6_6}_3_2=36(cm 3 ) 4 1 2_(24_8+8_7+7_24) =2_( )=832(cm 2 ) 1 8_8=64(cm 2 ) _5_4=1280(cm 2 ) =832_ _2 = =7424(cm 2 ) 86

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