ΛΥΣΕΙΣ ΣΧΟΛΙΚΩΝ ΑΣΚΗΣΕΩΝ Β ΓΥΜΝΑΣΙΟΥ 1 ΚΕΦΑΛΑΙΟ ΓΕΩΜΕΤΡΙΑ

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1.1 . 115

1.

, ;

2.

. ;

39

3.

)

) ( ) .

)

)

12 9 .

12

, 5 .

12 , 8, 7, 6, 4, 3 ;

8 7 6 4 3 1.2 . 117-118

1.

1 . 6,2 m2 =62cm2620cm262000cm20,62cm2

2. 6,2 mm2 =62cm2620cm20,62cm20,062cm2

3. 6,2 cm2 =62m20,62m2620m20,00062m2

4. 6,2 cm2 =620mm26200mm20,62mm20,00062mm2

5. 6,2 m2 =62dm2620dm262000dm20,062dm2

6. 6,2 mm20,0000062m20,00062m20,062m20,0062m2

1. 6,2 m2 = 6,2 (10000 cm2 = 62000 cm2

2. 6,2 mm2 = 6,2:100 cm2 = 0,062cm2 3. 6,2 cm2 = 6,2:10000 m2 = 0,00062m2 4. 6,2 cm2 = 6,2 (100 mm2 = 620mm2 A5. 6,2 m2 = 6,2 (100 dm2 = 620dm2 B

6. 6,2 mm2 = 6,2 : 1000000m2 =0,0000062m2 A2.

:

:

1 . m2 dm2 / 100 100 10

2. dm2 cm2 100 / 100 10

3. cm2 mm2 100 10 / 100

4. dm2 m2 / 100 100 10

5. cm2 dm2 / 10000 / 100 100

6. mm2 cm2 100 / 100 10

7. m2 cm2 100 / 10000 10000

8. m2 mm2 / 1000000 100000 1000

9. cm2 m2 100 10000 / 10000

10 . mm2 dm2 100 / 10000 10000

1( 2( 3( 4( 5(

6( 7( 8( 9( 10(

1. m2 32 cm2 , 312 cm2 , 127 km2 , 710 dm2 ,

12720 mm2 , 212 dm2 , 1280 mm2 , 79 km2 ,

32cm2 = 32 : 10000 m2 = 0,0032 m2

312 cm2 = 312 : 10000 m2 = 0,0312 m2 127km2 = 127( 1.000.000 m2 = 127.000.000m2710dm2 = 710 : 100 m2 = 7,1m212720mm2 = 12720 : 1.000.000m2 = 0,01272m2212dm2 = 212 : 100 m2 = 2,12m21280mm2 = 1280 : 1.000.000m2 = 0,00128m279km2 = 79( 1.000.000 m2 = 79.000.000m22.

cm2 12 m2 , 175 dm2 , 456 m2 , 136 m2 ,

3 km2 , 1750 mm2, 256 km2

12m2 = 12 (10000 cm2 = 120.000 cm2

175 dm2 = 175(100 cm2 = 17.500 cm2456m2 = 456 (10000 cm2 = 4.560.000 cm2

136 m2 = 136 (10000 cm2 = 1.360.000 cm23 km2 = 3(10000 000000 cm2= 30.000.000.000cm2 1750 mm2 = 1750 : 100 cm2 = 17,5 cm2256 km2 = 256(10000 000000 cm2 = 2.560.000.000.000cm2

3.

mm2 12 km2 , 431 m2 , 17 dm2 , 236 cm2 12 km2 = 12(1.000.000.000.000 mm2 = 12.000.000.000.000 mm2431 m2 = 431 (1.000.000 mm2 = 431.000.000 mm217 dm2 = 17 (10000 mm2 = 170.000 mm2236 cm2 = 236(100 mm2 = 23.600 mm24.

km2 7233 mm2 , 4321 cm2 , 6322 dm2 , 14632 mm2 , 560m2

7233 mm2 = 7233 : 1.000.000.000.000 km2 = 0, 000000007233 km24321 cm2 = 4321 : 10.000.000.000 km2 = 0,0000004321 km26322 dm2 = 6322 : 100.000.000 km2 = 0,00006322 km214632 mm2 = 14632 : 1.000.000.000.000 km2 = 0, 000000014632 km2560m2 = 560 : 1.000.000 = 0,00056 km25.

.

) 13850mm2 , 0,23 m2 , 0,48 m2 , 670cm2 , 13,7 dm2 ) 32 dm2 , 1,23 m2 , 23270 mm2 , 1356cm2

) 13850 mm2 = 13850 : 1.000.000m2 = 0,01385m2

670cm2 = 670 : 10.000 m2 = 0,067 m213,7 dm2 = 13,7 : 100 m2 = 0,137 m2

0,01385m2 < 0,067 m2 < 0,137m2 < 0,23m2 < 0,48m2

13850mm2 < 670cm2 < 13,7dm2 < 0,23m2 < 0,48m2 ) 32 dm2 = 32 : 100 m2 = 0,32 m223270 mm2 = 232700 : 1.000.000m2 = 0,02327m21356cm2 = 1356 : 10.000 m2 = 0,1356 m2 0,02327m2 < 0,1356 m2< 0,32m2 < 1,23m2

23270mm2 < 1356 cm2 < 32dm2 < 1,23m2 6. :

)

)

)

)

)

) m2 ) km2 ) ) cm2 ) cm2

1.3 . 123-124 -125-126

1.

1. : 3 6 9

2. : 61218

3. :121821

4. : 912 4,5

5. : 912 4,5

6. :121821

7. :22,51827

8. :22,51821

1. 3.

32 = 9. 2. 3 6.

3( 6 = 18. 3. 6 3.

3( 6 = 18. 4. 6 3.

3( 6 = 9. 5. 3 3.

3( 3 = 4,5.

6. 9 3, 3.

(3 + 9) 3 = 19.

7. 9 6, 3.

(6 + 9) 3 = 22,5.

8. 9 3, 3.

(3 + 9) 3 = 18.

: 2

2.

1.

/ 24 9 18

2 . x

5,5 9 4,5

3.

/ 24 12 32

4. x = 4 6 5

5.

6.

32 16 20

7.

4 5 6

8. /

16cm2

.

: 4 6 8

9.

: 5 4 8

10.

: 16 20 17,5

11.

12cm2

,

24 16 18

1. ( = 6(3 = 18, 2. : 18 = 4(x x = 18: 4 = 4,5, 3. ( = 8(3 = 24, 4. : 24 = 6(x x = 24: 6 = 4, 5. ,

6. = = 20, 7. 20 = x = 5,

8. 16 = 10( = 1,6

( ) = = = 4,

9. ( = 1( 8 = 8, 10. = = 16, 11.

. 12 = (

() = = = = = 6

() + () = 12 + 6 = 18,

1.

60 cm,

x, = 4x

60 = 4x

x = 15 cm

= 152 = 225 cm2 2.

21 cm

30cm. .

21( 30 = 630cm2 20( 630 = 12600 cm2 = 12600 : 10000 m2 = 1,26m23.

4( 12 = 48

4.

. =

) .

) .

)

x,

= x2 .

() = = = = x2

() = () )

() = = =

5.

, x = 5 cm. x.

x = 5 T 5 8

1 = 5( 8 = 40 cm2 x = 5 cm 5 6 cm 52 = 25 cm2

= 15 cm2 2 = 25 + 15 = 40 cm2 1 = 2.

:

1 = x( x + 3) = x2 + 3x

2 = + = x2 + = x2 + 3x x 1 = 2 . 6.

.

12 cm 20cm 4cm,

= = 64 cm2 = 64 cm27.

40m 25m. . 0,6 m 0,8m. . 12 m2 .

= 25 ( 40 = 1000 m2 1

0,8 ( 25 = 20m2 2 0,6 ( 40 = 24m2 1 2,

.

= 12 + () =

= 10002024 + 0,48 =

= 956,48 m28.

. .

, .

.

.

, .

9.

)

) x

.

)

,

= = 18 m = = 30x

, .

)

x = 18 m. = 18 x m2 . 30(1818x

18x = (30(1818x )

4(18x = 4((30(1818x )

72x = 38018x 72x + 18 x = 540

90x = 540

x = 6 m

10.

.

)

)

)

,

= = . ,

)

x , = = = .

= 2 ( = .

.

() = x2

= () = 11.

1 cm . 12

1 = 15 = 15 cm2 2 = 12 = 12 cm2 3 = 7,5 = 7,5 cm2 4 = 16 = 16 cm2 5 = 16 = 16 cm2 6 = 15 = 15 cm2 7 = 9 = 9 cm2 8 = 16 = 16 cm2 9 = 18,5 = 18,5 cm2 10 = 10 = 10 cm2 11 = 11 = 11 cm2 12 = 22 = 22 cm2

12.

.

= 5 cm , = 3cm = 6cm,

() = () + () =

= + =

= + = 7,5 + 15 = 22,5 cm2 13.

x

: 4x = 40 x = 10 cm : x 2 = 36 x = 6 cm : = 20 2x = 20 x = 10 cm

: = 18 x2 = 36 x = 6 cm

14.

1 = 12 (5 = 60 cm2 , E2 = = 34 cm2 , E3 = = 32 cm2E4 = = 24 cm2 E5 = 92 = 81 cm2