ΛΥΣΕΙΣ ΣΧΟΛΙΚΩΝ ΑΣΚΗΣΕΩΝ Β ΓΥΜΝΑΣΙΟΥ 1 ΚΕΦΑΛΑΙΟ ΓΕΩΜΕΤΡΙΑ

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<p>1.1 . 115</p> <p>1. </p> <p> , ; </p> <p>2.</p> <p> . ; </p> <p> 39</p> <p>3.</p> <p>) </p> <p>) ( ) .</p> <p>) </p> <p>) </p> <p> 12 9 . </p> <p> 12 </p> <p> , 5 . </p> <p> 12 , 8, 7, 6, 4, 3 ; </p> <p> 8 7 6 4 3 1.2 . 117-118 </p> <p>1.</p> <p>1 . 6,2 m2 =62cm2620cm262000cm20,62cm2</p> <p>2. 6,2 mm2 =62cm2620cm20,62cm20,062cm2</p> <p>3. 6,2 cm2 =62m20,62m2620m20,00062m2</p> <p>4. 6,2 cm2 =620mm26200mm20,62mm20,00062mm2</p> <p>5. 6,2 m2 =62dm2620dm262000dm20,062dm2</p> <p>6. 6,2 mm20,0000062m20,00062m20,062m20,0062m2</p> <p>1. 6,2 m2 = 6,2 (10000 cm2 = 62000 cm2 </p> <p>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 </p> <p>6. 6,2 mm2 = 6,2 : 1000000m2 =0,0000062m2 A2. </p> <p> :</p> <p> : </p> <p>1 . m2 dm2 / 100 100 10</p> <p>2. dm2 cm2 100 / 100 10</p> <p>3. cm2 mm2 100 10 / 100</p> <p>4. dm2 m2 / 100 100 10</p> <p>5. cm2 dm2 / 10000 / 100 100</p> <p>6. mm2 cm2 100 / 100 10 </p> <p>7. m2 cm2 100 / 10000 10000</p> <p>8. m2 mm2 / 1000000 100000 1000 </p> <p>9. cm2 m2 100 10000 / 10000</p> <p>10 . mm2 dm2 100 / 10000 10000</p> <p>1( 2( 3( 4( 5( </p> <p>6( 7( 8( 9( 10( </p> <p>1. m2 32 cm2 , 312 cm2 , 127 km2 , 710 dm2 ,</p> <p>12720 mm2 , 212 dm2 , 1280 mm2 , 79 km2 , </p> <p>32cm2 = 32 : 10000 m2 = 0,0032 m2</p> <p>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.</p> <p> cm2 12 m2 , 175 dm2 , 456 m2 , 136 m2 ,</p> <p>3 km2 , 1750 mm2, 256 km2 </p> <p>12m2 = 12 (10000 cm2 = 120.000 cm2 </p> <p>175 dm2 = 175(100 cm2 = 17.500 cm2456m2 = 456 (10000 cm2 = 4.560.000 cm2 </p> <p>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 </p> <p>3.</p> <p> 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.</p> <p> km2 7233 mm2 , 4321 cm2 , 6322 dm2 , 14632 mm2 , 560m2 </p> <p> 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.</p> <p> . </p> <p>) 13850mm2 , 0,23 m2 , 0,48 m2 , 670cm2 , 13,7 dm2 ) 32 dm2 , 1,23 m2 , 23270 mm2 , 1356cm2 </p> <p> ) 13850 mm2 = 13850 : 1.000.000m2 = 0,01385m2 </p> <p>670cm2 = 670 : 10.000 m2 = 0,067 m213,7 dm2 = 13,7 : 100 m2 = 0,137 m2 </p> <p> 0,01385m2 &lt; 0,067 m2 &lt; 0,137m2 &lt; 0,23m2 &lt; 0,48m2 </p> <p> 13850mm2 &lt; 670cm2 &lt; 13,7dm2 &lt; 0,23m2 &lt; 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 &lt; 0,1356 m2&lt; 0,32m2 &lt; 1,23m2 </p> <p> 23270mm2 &lt; 1356 cm2 &lt; 32dm2 &lt; 1,23m2 6. :</p> <p>) </p> <p>) </p> <p>) </p> <p>) </p> <p>) </p> <p> ) m2 ) km2 ) ) cm2 ) cm2 </p> <p>1.3 . 123-124 -125-126</p> <p>1.</p> <p>1. : 3 6 9</p> <p>2. : 61218</p> <p>3. :121821</p> <p>4. : 912 4,5</p> <p>5. : 912 4,5</p> <p>6. :121821</p> <p>7. :22,51827</p> <p>8. :22,51821</p> <p>1. 3. </p> <p> 32 = 9. 2. 3 6. </p> <p> 3( 6 = 18. 3. 6 3.</p> <p> 3( 6 = 18. 4. 6 3.</p> <p> 3( 6 = 9. 5. 3 3.</p> <p> 3( 3 = 4,5. </p> <p>6. 9 3, 3.</p> <p> (3 + 9) 3 = 19. </p> <p>7. 9 6, 3.</p> <p> (6 + 9) 3 = 22,5. </p> <p>8. 9 3, 3.</p> <p> (3 + 9) 3 = 18. </p> <p> : 2 </p> <p>2. </p> <p>1. </p> <p> / 24 9 18</p> <p>2 . x </p> <p> 5,5 9 4,5</p> <p>3. </p> <p> / 24 12 32</p> <p>4. x = 4 6 5</p> <p>5. </p> <p>6. </p> <p> 32 16 20</p> <p>7. </p> <p> 4 5 6</p> <p>8. / </p> <p> 16cm2 </p> <p> . </p> <p> : 4 6 8</p> <p>9. </p> <p> : 5 4 8</p> <p>10. </p> <p> : 16 20 17,5</p> <p> 11. </p> <p> 12cm2 </p> <p> , </p> <p> 24 16 18</p> <p>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. , </p> <p>6. = = 20, 7. 20 = x = 5, </p> <p>8. 16 = 10( = 1,6 </p> <p> ( ) = = = 4, </p> <p>9. ( = 1( 8 = 8, 10. = = 16, 11. </p> <p> . 12 = ( </p> <p> () = = = = = 6 </p> <p> () + () = 12 + 6 = 18, </p> <p>1. </p> <p> 60 cm, </p> <p> x, = 4x </p> <p> 60 = 4x </p> <p> x = 15 cm </p> <p> = 152 = 225 cm2 2.</p> <p> 21 cm </p> <p>30cm. . </p> <p> 21( 30 = 630cm2 20( 630 = 12600 cm2 = 12600 : 10000 m2 = 1,26m23.</p> <p> 4( 12 = 48 </p> <p>4.</p> <p> . = </p> <p>) .</p> <p>) .</p> <p>) </p> <p> x, </p> <p> = x2 . </p> <p>() = = = = x2 </p> <p> () = () ) </p> <p> () = = = </p> <p>5.</p> <p> , x = 5 cm. x.</p> <p> x = 5 T 5 8 </p> <p>1 = 5( 8 = 40 cm2 x = 5 cm 5 6 cm 52 = 25 cm2 </p> <p> = 15 cm2 2 = 25 + 15 = 40 cm2 1 = 2.</p> <p> : </p> <p> 1 = x( x + 3) = x2 + 3x </p> <p> 2 = + = x2 + = x2 + 3x x 1 = 2 . 6.</p> <p> . </p> <p> 12 cm 20cm 4cm, </p> <p> = = 64 cm2 = 64 cm27.</p> <p> 40m 25m. . 0,6 m 0,8m. . 12 m2 . </p> <p> = 25 ( 40 = 1000 m2 1 </p> <p>0,8 ( 25 = 20m2 2 0,6 ( 40 = 24m2 1 2, </p> <p> .</p> <p> = 12 + () = </p> <p> = 10002024 + 0,48 = </p> <p> = 956,48 m28.</p> <p> . .</p> <p> , .</p> <p> .</p> <p> .</p> <p>, . </p> <p>9.</p> <p>) </p> <p>) x </p> <p> . </p> <p>) </p> <p> , </p> <p> = = 18 m = = 30x </p> <p> , . </p> <p>) </p> <p> x = 18 m. = 18 x m2 . 30(1818x </p> <p> 18x = (30(1818x ) </p> <p> 4(18x = 4((30(1818x ) </p> <p> 72x = 38018x 72x + 18 x = 540 </p> <p> 90x = 540 </p> <p> x = 6 m </p> <p>10.</p> <p> .</p> <p>) </p> <p>) </p> <p> ) </p> <p> , </p> <p> = = . , </p> <p>) </p> <p> x , = = = .</p> <p> = 2 ( = .</p> <p> . </p> <p> () = x2</p> <p> = () = 11.</p> <p> 1 cm . 12 </p> <p> 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 </p> <p>12.</p> <p> . </p> <p> = 5 cm , = 3cm = 6cm, </p> <p> () = () + () = </p> <p> = + = </p> <p> = + = 7,5 + 15 = 22,5 cm2 13.</p> <p> x </p> <p> : 4x = 40 x = 10 cm : x 2 = 36 x = 6 cm : = 20 2x = 20 x = 10 cm </p> <p> : = 18 x2 = 36 x = 6 cm </p> <p>14. </p> <p> 1 = 12 (5 = 60 cm2 , E2 = = 34 cm2 , E3 = = 32 cm2E4 = = 24 cm2 E5 = 92 = 81 cm2 E6 = = 12,5 cm215.</p> <p> .</p> <p> = 172 = 289 </p> <p> = = 30 </p> <p> = 2894 ( 30 = 169 16.</p> <p> . </p> <p>) </p> <p>) </p> <p>) </p> <p> 2 : = 2,5 ( 4,5 = 11,25 m 2 </p> <p> : = 2,5 ( 3 = 7,5 m 2 1 : = ( 1,5 + 2,5) ( 3 = 12 m 2 </p> <p> : = 3( 3 = 9 m 2 WC : = 3( 1,5 = 4,5 m 2 : = 4( 8,5 = 34 m 2 : = 3( 4 = 12m 2 : ( 3 + 1,5) (1,5 = 6,75</p> <p> : 3( 1,5 = 4,5 101,5 cm2</p> <p> 13,5 ( 11,5 = 155,25. </p> <p> 53,75 </p> <p>17.</p> <p> 20.000 . </p> <p>) </p> <p>) </p> <p> 2,5m2 ; </p> <p> ) </p> <p> , . </p> <p>50( 44 = 2200 m2 </p> <p> = 640m2 = 2200 m2 + 640m2 = 2840 m2 =</p> <p> = 2840 : 1000 = </p> <p> = 2,84 </p> <p> = 2,84 ( 20000 =56800 ) </p> <p> 2840 : 2,5 = 1136 </p> <p> , </p> <p> :</p> <p>1. </p> <p>2. 100cm2 </p> <p>3. </p> <p>4. </p> <p> .</p> <p> 2 3 1, : , 100 m2 , 400 m2 200 m2 ( ( ) . </p> <p>1.4 . 130-131 </p> <p>1. </p> <p> 1 4, </p> <p>x =7cm</p> <p>9cm10cm12cm</p> <p>x =2cm</p> <p>3cm4cm5cm</p> <p>x =14 cm</p> <p>20 cm24 cm30 cm</p> <p> =</p> <p> = = 15</p> <p> = 8</p> <p> = 13</p> <p> = 10 = 12</p> <p> = 13 = 8</p> <p> = 9</p> <p>1. x2 = 62 + 82 = 36 + 64 = 100 x = 10 2. x2 = 52 42 =2516 = 9 x = 3 3 . x2 = 262 102 = 676100 = 576 x = 24 4. 172 = 2 + 2 289 = 2 + 2 = 15 = 8 </p> <p>1. </p> <p> 259 = 16 m2 5,76 + 1 = 6,76 m2 10,64 = 0,36 m22.</p> <p>242 + 72 = 576 + 49 = 625 252 = 625 242 + 72 = 252 </p> <p> 25 162 + 122 = 256 + 144 = 400 202 = 400 162 + 122 = 202 </p> <p> 20 152 + 82 = 225 + 64 = 289 172 = 289 152 + 82 = 172 </p> <p> 173.</p> <p>) 6cm, 8cm 10cm. </p> <p>) </p> <p> . </p> <p> ) </p> <p>62 + 82 = 36 + 64 = 100 102 = 100 62 + 82 = 102 </p> <p> 10 ) 12 cm, 16cm, 20cm. </p> <p> 162 + 122 = 256 + 144 = 400 202 = 400 162 + 122 = 202 </p> <p> 20 3 , 4 , 5 </p> <p>32 + 42 = 52 , </p> <p> 5.</p> <p>4.</p> <p> = = 10dm </p> <p> = 12dm . </p> <p> . </p> <p> , </p> <p> = 6dm. </p> <p>2 = 2 2 2 = 102 62 = 100 36 = 64. </p> <p> 64dm2 5.</p> <p>2 = 2 + 2 </p> <p>2 = 12 + 2,12 = 1 + 4,41 = 5,41</p> <p> 5,41 m2 6. </p> <p>( ), </p> <p> = 30 cm </p> <p> = 40 cm. </p> <p> = 50 cm. </p> <p> ; </p> <p> 2 + 2 = 302 + 402 = 900 + 1600 = 2500</p> <p>2 = 502 = 2500 </p> <p> 2 + 2 = 2, </p> <p>7.</p> <p> 12 dm 16 dm. </p> <p> .</p> <p> = 8dm = 6dm </p> <p>2 = 2 + 2 2 = 82 + 62 = 64 + 36 = 100. </p> <p> = 10 </p> <p> , </p> <p> = 4( 10 = 40dm 4(), 4 .</p> <p> . </p> <p> () = = = 24 dm2 </p> <p> = 4( 24 = 96dm2 8.</p> <p> = = 5 m , = 7m = 13 m . x </p> <p> = = 5m = = x .</p> <p> , = . </p> <p> = = 7 m .</p> <p> = 13, = 137, + = 6.</p> <p> , = = 3 </p> <p>2 = 2 + 2 52 = x2 + 32 </p> <p> 25 = x2 + 9 x2 = 16 x = 4 9.</p> <p> , , . </p> <p>2 = 2 2 2 = 172 82 2 = 28964 </p> <p> 2 = 225 </p> <p> = 15 m </p> <p>2 = 2 +2 2 = 122 + 92 </p> <p> 2 = 144 + 81 </p> <p> 2 = 225 </p> <p> = 15m = 17 m, . </p> <p> ( = 90) . , . , ; </p> <p>_1437456726.unknown</p> <p>_1437466734.unknown</p> <p>_1437467476.unknown</p> <p>_1437480407.unknown</p> <p>_1437480484.unknown</p> <p>_1437482942.unknown</p> <p>_1437484644.unknown</p> <p>_1437536101.unknown</p> <p>_1437484625.unknown</p> <p>_1437482905.unknown</p> <p>_1437480434.unknown</p> <p>_1437470970.unknown</p> <p>_1437472436.unknown</p> <p>_1437467774.unknown</p> <p>_1437467134.unknown</p> <p>_1437467353.unknown</p> <p>_1437467423.unknown</p> <p>_1437467274.unknown</p> <p>_1437466804.unknown</p> <p>_1437467033.unknown</p> <p>_1437466770.unknown</p> <p>_1437463914.unknown</p> <p>_1437465615.unknown</p> <p>_1437466660.unknown</p> <p>_1437465733.unknown</p> <p>_1437465859.unknown</p> <p>_1437465547.unknown</p> <p>_1437465580.unknown</p> <p>_1437464325.unknown</p> <p>_1437457614.unknown</p> <p>_1437459055.unknown</p> <p>_1437460185.unknown</p> <p>_1437457766.unknown</p> <p>_1437456780.unknown</p> <p>_1437457284.unknown</p> <p>_1437456749.unknown</p> <p>_1437453500.unknown</p> <p>_1437454558.unknown</p> <p>_1437456577.unknown</p> <p>_1437456621.unknown</p> <p>_1437456536.unknown</p> <p>_1437454505.unknown</p> <p>_1437454537.unknown</p> <p>_1437453919.unknown</p> <p>_1437453095.unknown</p> <p>_1437453263.unknown</p> <p>_1437453464.unknown</p> <p>_1437451662.unknown</p> <p>_1437451725.unknown</p> <p>_1437452901.unknown</p> <p>_1436281728.unknown</p> <p>_1436293051.unknown</p> <p>_1436344777.unknown</p> <p>_1436281707.unknown</p> <p>_1436260356.unknown</p> <p>_1436281650.unknown</p>