164:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000 Cuerpos geométricos :@0.073089:0.043661:0.266504:0.043661:0.266504:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejemplo 3:@0.293660:0.136836:0.369443:0.136836:0.369443:0.120167:0.293660:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Una empresa de chocolates tiene dos tipos de empaques para guardar sus productos y :@0.293660:0.161702:0.931440:0.161702:0.931440:0.145268:0.293660:0.145268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 desean saber cuánto material se necesita para fabricar cada uno de ellos y cuál sería su :@0.293660:0.178344:0.930505:0.178344:0.930505:0.161910:0.293660:0.161910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 volumen.:@0.293660:0.194986:0.361870:0.194986:0.361870:0.178552:0.293660:0.178552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Solución:@0.293660:0.219851:0.359794:0.219851:0.359794:0.203182:0.293660:0.203182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Primero, debemos hallar el área superficial del empaque 1. Para esto, desarrollamos el :@0.293660:0.244717:0.930989:0.244717:0.930989:0.228283:0.293660:0.228283:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 plano del empaque 1, que corresponde a un prisma.:@0.293660:0.261359:0.673748:0.261359:0.673748:0.244925:0.293660:0.244925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La base es triangular, por lo cual:@0.293660:0.286224:0.524601:0.286224:0.524601:0.269791:0.293660:0.269791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A :@0.293660:0.314626:0.311903:0.314605:0.311903:0.298199:0.293660:0.298220:0.000000:0.000000:0.000000 B:@0.303478:0.317777:0.308629:0.317777:0.308629:0.308213:0.303478:0.308213:0.000000 5:@0.311830:0.314050:0.327163:0.314050:0.327163:0.300335:0.311830:0.300335:0.000000 :@0.327071:0.314605:0.331102:0.314605:0.331102:0.298171:0.327071:0.298171:0.000000 9 cm 6 cm:@0.334797:0.308759:0.412690:0.308759:0.412690:0.295313:0.334797:0.295313:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.367463:0.308305:0.380009:0.308305:0.380009:0.297083:0.367463:0.297083:0.000000 2:@0.369650:0.322103:0.377816:0.322103:0.377816:0.307163:0.369650:0.307163:0.000000 27 cm:@0.416356:0.314605:0.484500:0.314605:0.484500:0.298171:0.416356:0.298171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.420314:0.314050:0.435647:0.314050:0.435647:0.300335:0.420314:0.300335:0.000000 2:@0.484378:0.308541:0.489615:0.308541:0.489615:0.298960:0.484378:0.298960:0.000000 Rectángulo 1: 15 cm 9 cm 135 cm:@0.293660:0.339467:0.613951:0.339467:0.613951:0.323033:0.293660:0.323033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.396906:0.339467:0.406791:0.339467:0.406791:0.323061:0.396906:0.323061:0.000000 r:@0.406719:0.342639:0.409799:0.342639:0.409799:0.333075:0.406719:0.333075:0.000000 5:@0.413717:0.338912:0.429050:0.338912:0.429050:0.325197:0.413717:0.325197:0.000000 3:@0.481732:0.338912:0.497065:0.338912:0.497065:0.325197:0.481732:0.325197:0.000000 5:@0.540856:0.338912:0.556189:0.338912:0.556189:0.325197:0.540856:0.325197:0.000000 2:@0.613823:0.333403:0.619059:0.333403:0.619059:0.323822:0.613823:0.323822:0.000000 Los rectángulos 2 y 3 son iguales. :@0.293660:0.364328:0.538116:0.364328:0.538116:0.347894:0.293660:0.347894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Hallamos por medio del teorema de Pitágoras el lado que hace :@0.293660:0.389193:0.753783:0.389193:0.753783:0.372759:0.293660:0.372759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 falta de dichos rectángulos.:@0.293660:0.405835:0.492234:0.405835:0.492234:0.389401:0.293660:0.389401:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.293660:0.430701:0.302919:0.430701:0.302919:0.414295:0.293660:0.414295:0.000000 (6 cm) (4,5 cm):@0.302845:0.430701:0.466760:0.430693:0.466760:0.414259:0.302845:0.414267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.306803:0.430146:0.322136:0.430146:0.322136:0.416430:0.306803:0.416430:0.000000 2:@0.380688:0.424629:0.385925:0.424629:0.385925:0.415048:0.380688:0.415048:0.000000 1:@0.389836:0.430138:0.405170:0.430138:0.405170:0.416423:0.389836:0.416423:0.000000 2:@0.466616:0.424629:0.471853:0.424629:0.471853:0.415048:0.466616:0.415048:0.000000 a:@0.293660:0.455554:0.302919:0.455554:0.302919:0.439148:0.293660:0.439148:0.000000 (36 cm 20,25 cm ) 7,5 cm:@0.302845:0.455554:0.560180:0.455554:0.560180:0.439120:0.302845:0.439120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.306803:0.454999:0.322136:0.454999:0.322136:0.441283:0.306803:0.441283:0.000000 2:@0.384793:0.449490:0.390030:0.449490:0.390030:0.439909:0.384793:0.439909:0.000000 1:@0.393941:0.454999:0.409274:0.454999:0.409274:0.441283:0.393941:0.441283:0.000000 2:@0.478931:0.449490:0.484168:0.449490:0.484168:0.439909:0.478931:0.439909:0.000000 5:@0.492865:0.454999:0.508198:0.454999:0.508198:0.441283:0.492865:0.441283:0.000000 Por lo tanto, el área de los rectángulos 2 y 3 es A 15 cm 7,5 cm 112,5 cm:@0.293662:0.480419:0.873010:0.480416:0.873010:0.463982:0.293662:0.463986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 r 2:@0.640409:0.483588:0.648769:0.484849:0.648769:0.475268:0.640409:0.474007:0.000000:0.000000:0.000000 5:@0.652675:0.479861:0.668008:0.479861:0.668008:0.466145:0.652675:0.466145:0.000000 3:@0.720690:0.479861:0.736023:0.479861:0.736023:0.466145:0.720690:0.466145:0.000000 5:@0.791834:0.479861:0.807167:0.479861:0.807167:0.466145:0.791834:0.466145:0.000000 2:@0.872878:0.474352:0.878115:0.474352:0.878115:0.464771:0.872878:0.464771:0.000000 Finalmente, el área superficial de un prisma: A=2 + El área de cada rectángulo lateral.:@0.293660:0.505278:0.916032:0.505278:0.916032:0.488844:0.293660:0.488844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.644042:0.505278:0.653927:0.505278:0.653927:0.488872:0.644042:0.488872:0.000000 B:@0.653867:0.508450:0.659018:0.508450:0.659018:0.498885:0.653867:0.498885:0.000000 A:@0.293650:0.530143:0.303535:0.530143:0.303535:0.513737:0.293650:0.513737:0.000000 2(27cm ) 135 cm 112,5 cm 112,5 cm 414 cm:@0.303461:0.530143:0.738676:0.530139:0.738676:0.513706:0.303461:0.513709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.307419:0.529589:0.322752:0.529589:0.322752:0.515873:0.307419:0.515873:0.000000 2:@0.381249:0.524076:0.386485:0.524076:0.386485:0.514495:0.381249:0.514495:0.000000 1:@0.395181:0.529585:0.410514:0.529585:0.410514:0.515869:0.395181:0.515869:0.000000 2:@0.468158:0.524076:0.473394:0.524076:0.473394:0.514495:0.468158:0.514495:0.000000 1:@0.477306:0.529585:0.492639:0.529585:0.492639:0.515869:0.477306:0.515869:0.000000 2:@0.562296:0.524076:0.567532:0.524076:0.567532:0.514495:0.562296:0.514495:0.000000 1:@0.571444:0.529585:0.586777:0.529585:0.586777:0.515869:0.571444:0.515869:0.000000 2:@0.656434:0.524076:0.661670:0.524076:0.661670:0.514495:0.656434:0.514495:0.000000 5:@0.665580:0.529585:0.680914:0.529585:0.680914:0.515869:0.665580:0.515869:0.000000 2:@0.738547:0.524076:0.743784:0.524076:0.743784:0.514495:0.738547:0.514495:0.000000 Luego, se halla el volumen del empaque 1. Con este fin, utilizamos la fórmula :@0.293660:0.555000:0.854443:0.555000:0.854443:0.538566:0.293660:0.538566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 V:@0.293660:0.579866:0.302772:0.579866:0.302772:0.563460:0.293660:0.563460:0.000000 , donde 27 cm y :@0.302643:0.579866:0.530183:0.579862:0.530183:0.563428:0.302643:0.563432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.306103:0.579311:0.321437:0.579311:0.321437:0.565595:0.306103:0.565595:0.000000 A:@0.324713:0.579866:0.334598:0.579866:0.334598:0.563460:0.324713:0.563460:0.000000 B:@0.334444:0.583034:0.339595:0.583034:0.339595:0.573470:0.334444:0.573470:0.000000 3:@0.342978:0.579307:0.358311:0.579307:0.358311:0.565592:0.342978:0.565592:0.000000 h:@0.361588:0.579862:0.371086:0.579862:0.371086:0.563456:0.361588:0.563456:0.000000 A:@0.428701:0.579862:0.438585:0.579862:0.438585:0.563456:0.428701:0.563456:0.000000 B:@0.438435:0.583034:0.443586:0.583034:0.443586:0.573470:0.438435:0.573470:0.000000 5:@0.446967:0.579307:0.462301:0.579307:0.462301:0.565592:0.446967:0.565592:0.000000 2:@0.509616:0.573798:0.514853:0.573798:0.514853:0.564217:0.509616:0.564217:0.000000 h :@0.529613:0.579862:0.542295:0.579862:0.542295:0.563456:0.529613:0.563456:0.000000:0.000000 5:@0.541817:0.579307:0.557150:0.579307:0.557150:0.565592:0.541817:0.565592:0.000000 15 cm, por lo tanto, 27 cm 15 cm 405 cm .:@0.556966:0.579862:0.926911:0.579862:0.926911:0.563428:0.556966:0.563428:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 V:@0.700769:0.579862:0.709880:0.579862:0.709880:0.563456:0.700769:0.563456:0.000000 5:@0.713207:0.579307:0.728540:0.579307:0.728540:0.565592:0.713207:0.565592:0.000000 2:@0.775841:0.573798:0.781078:0.573798:0.781078:0.564217:0.775841:0.564217:0.000000 3:@0.784444:0.579307:0.799778:0.579307:0.799778:0.565592:0.784444:0.565592:0.000000 5:@0.847103:0.579307:0.862436:0.579307:0.862436:0.565592:0.847103:0.565592:0.000000 3:@0.918566:0.573798:0.923803:0.573798:0.923803:0.564217:0.918566:0.564217:0.000000 Para hallar el área superficial del empaque 2, debemos desarrollar el plano del empaque :@0.293665:0.604728:0.931460:0.604728:0.931460:0.588294:0.293665:0.588294:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2, que corresponde a una pirámide.:@0.293665:0.621370:0.550608:0.621370:0.550608:0.604936:0.293665:0.604936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Como la base es cuadrada, usamos la siguiente fórmula::@0.293665:0.646235:0.697953:0.646235:0.697953:0.629801:0.293665:0.629801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.293665:0.671101:0.303550:0.671101:0.303550:0.654695:0.293665:0.654695:0.000000 B :@0.303478:0.674261:0.310518:0.674261:0.310518:0.664696:0.303478:0.664696:0.000000:0.000000 5:@0.310484:0.670534:0.325818:0.670534:0.325818:0.656818:0.310484:0.656818:0.000000 :@0.325726:0.674261:0.327657:0.674261:0.327657:0.664696:0.325726:0.664696:0.000000 7 cm 7 cm 49 cm:@0.327618:0.671088:0.490854:0.671088:0.490854:0.654654:0.327618:0.654654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.367543:0.670534:0.382877:0.670534:0.382877:0.656818:0.367543:0.656818:0.000000 5:@0.426668:0.670534:0.442001:0.670534:0.442001:0.656818:0.426668:0.656818:0.000000 2:@0.490735:0.665024:0.495972:0.665024:0.495972:0.655443:0.490735:0.655443:0.000000 Para los triángulos, primero hallamos por medio del teorema de Pitágoras.:@0.293660:0.695950:0.841210:0.695950:0.841210:0.679516:0.293660:0.679516:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.563529:0.695950:0.572788:0.695950:0.572788:0.679544:0.563529:0.679544:0.000000 a:@0.293660:0.720816:0.302919:0.720816:0.302919:0.704410:0.293660:0.704410:0.000000 (18 cm):@0.302845:0.720816:0.389721:0.720811:0.389721:0.704377:0.302845:0.704382:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.306803:0.720261:0.322136:0.720261:0.322136:0.706545:0.306803:0.706545:0.000000 2 :@0.389590:0.714747:0.397134:0.714747:0.397134:0.705166:0.389590:0.705166:0.000000:0.000000 1:@0.397084:0.720256:0.412417:0.720256:0.412417:0.706540:0.397084:0.706540:0.000000 :@0.412325:0.714747:0.414675:0.714747:0.414675:0.705166:0.412325:0.705166:0.000000 (3,5 cm) :@0.414629:0.720811:0.481493:0.720811:0.481493:0.704377:0.414629:0.704377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.472224:0.714747:0.477461:0.714747:0.477461:0.705166:0.472224:0.705166:0.000000 a:@0.293665:0.745676:0.302924:0.745676:0.302924:0.729270:0.293665:0.729270:0.000000 324 cm:@0.302850:0.745676:0.389021:0.745673:0.389021:0.729239:0.302850:0.729243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.306808:0.745122:0.322141:0.745122:0.322141:0.731406:0.306808:0.731406:0.000000 2 :@0.388899:0.739609:0.396443:0.739609:0.396443:0.730028:0.388899:0.730028:0.000000:0.000000 1:@0.396391:0.745118:0.411724:0.745118:0.411724:0.731402:0.396391:0.731402:0.000000 12,25 cm:@0.411632:0.745673:0.481525:0.745673:0.481525:0.729239:0.411632:0.729239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 :@0.481389:0.739609:0.488976:0.739609:0.488976:0.730028:0.481389:0.730028:0.000000:0.000000 a:@0.293660:0.770535:0.302919:0.770535:0.302919:0.754128:0.293660:0.754128:0.000000 18,38 cm:@0.302845:0.770535:0.387979:0.770535:0.387979:0.754101:0.302845:0.754101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.306803:0.769980:0.322136:0.769980:0.322136:0.756264:0.306803:0.756264:0.000000 Esta se utiliza como la altura del triángulo para poder hallar su área.:@0.293660:0.795400:0.778411:0.795400:0.778411:0.778966:0.293660:0.778966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.293660:0.823802:0.303545:0.823802:0.303545:0.807396:0.293660:0.807396:0.000000 T:@0.303478:0.826966:0.308210:0.826966:0.308210:0.817401:0.303478:0.817401:0.000000 = :@0.308172:0.823793:0.323100:0.823793:0.323100:0.807360:0.308172:0.807360:0.000000:0.000000 7 cm 18,38 cm:@0.327963:0.817946:0.430284:0.817946:0.430284:0.804500:0.327963:0.804500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.360629:0.817492:0.373174:0.817492:0.373174:0.806270:0.360629:0.806270:0.000000 2:@0.375019:0.831291:0.383185:0.831291:0.383185:0.816351:0.375019:0.816351:0.000000 64,33 cm:@0.435110:0.823793:0.524201:0.823793:0.524201:0.807360:0.435110:0.807360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.439067:0.823239:0.454401:0.823239:0.454401:0.809523:0.439067:0.809523:0.000000 2:@0.524059:0.817730:0.529296:0.817730:0.529296:0.808149:0.524059:0.808149:0.000000 Reemplazamos la fórmula para el área superficial::@0.293660:0.848654:0.649730:0.848654:0.649730:0.832220:0.293660:0.832220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.293660:0.873520:0.303545:0.873520:0.303545:0.857114:0.293660:0.857114:0.000000 :@0.303471:0.873520:0.397362:0.873516:0.397362:0.857082:0.303471:0.857086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.307429:0.872965:0.322762:0.872965:0.322762:0.859249:0.307429:0.859249:0.000000 A:@0.326628:0.873520:0.336512:0.873520:0.336512:0.857114:0.326628:0.857114:0.000000 B:@0.336439:0.876688:0.341590:0.876688:0.341590:0.867124:0.336439:0.867124:0.000000 1 3:@0.345508:0.872961:0.393422:0.872961:0.393422:0.859246:0.345508:0.859246:0.000000:0.000000:0.000000 n:@0.364707:0.873516:0.374205:0.873516:0.374205:0.857110:0.364707:0.857110:0.000000 A :@0.397288:0.873516:0.433574:0.873516:0.433574:0.857110:0.397288:0.857110:0.000000:0.000000:0.000000:0.000000:0.000000 T:@0.407086:0.876688:0.411818:0.876688:0.411818:0.867124:0.407086:0.867124:0.000000 5:@0.415019:0.872961:0.430352:0.872961:0.430352:0.859246:0.415019:0.859246:0.000000 49 cm 4(63,33cm ) 306,32 cm:@0.433500:0.873516:0.690256:0.873516:0.690256:0.857082:0.433500:0.857082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.478394:0.867452:0.483631:0.867452:0.483631:0.857871:0.478394:0.857871:0.000000 1:@0.487542:0.872961:0.502875:0.872961:0.502875:0.859246:0.487542:0.859246:0.000000 2:@0.582281:0.867452:0.587518:0.867452:0.587518:0.857871:0.582281:0.857871:0.000000 5:@0.596213:0.872961:0.611547:0.872961:0.611547:0.859246:0.596213:0.859246:0.000000 2:@0.690117:0.867452:0.695354:0.867452:0.695354:0.857871:0.690117:0.857871:0.000000 Para el volumen, se tiene que, V:@0.293660:0.903700:0.521406:0.903700:0.521406:0.887267:0.293660:0.887267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 :@0.521137:0.903146:0.545490:0.903146:0.545490:0.889430:0.521137:0.889430:0.000000:0.000000:0.000000 1:@0.550878:0.896067:0.558228:0.896067:0.558228:0.882621:0.550878:0.882621:0.000000 3:@0.550470:0.909412:0.558636:0.909412:0.558636:0.894472:0.550470:0.894472:0.000000 (:@0.563629:0.903700:0.572465:0.903700:0.572465:0.887267:0.563629:0.887267:0.000000:0.000000 A:@0.572373:0.903700:0.582257:0.903700:0.582257:0.887294:0.572373:0.887294:0.000000 B :@0.582196:0.906873:0.589235:0.906873:0.589235:0.897308:0.582196:0.897308:0.000000:0.000000 3:@0.589202:0.903146:0.604535:0.903146:0.604535:0.889430:0.589202:0.889430:0.000000 ). Por lo tanto, :@0.604443:0.903700:0.724679:0.903700:0.724679:0.887267:0.604443:0.887267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.608401:0.903700:0.617899:0.903700:0.617899:0.887294:0.608401:0.887294:0.000000 V:@0.293655:0.923879:0.302767:0.923879:0.302767:0.907473:0.293655:0.907473:0.000000 (49 cm 18 cm) 294 cm .:@0.302693:0.923879:0.561034:0.923878:0.561034:0.907444:0.302693:0.907445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.306651:0.923324:0.321984:0.923324:0.321984:0.909608:0.306651:0.909608:0.000000 1:@0.331330:0.918032:0.338679:0.918032:0.338679:0.904586:0.331330:0.904586:0.000000 3:@0.330921:0.931376:0.339088:0.931376:0.339088:0.916436:0.330921:0.916436:0.000000 2:@0.397710:0.917814:0.402946:0.917814:0.402946:0.908233:0.397710:0.908233:0.000000 3:@0.406856:0.923324:0.422190:0.923324:0.422190:0.909608:0.406856:0.909608:0.000000 5:@0.479675:0.923324:0.495009:0.923324:0.495009:0.909608:0.479675:0.909608:0.000000 3:@0.552640:0.917814:0.557877:0.917814:0.557877:0.908233:0.552640:0.908233:0.000000 DBA 4 (Ev. 2) Expresa la misma medida con diferentes unidades según el contexto.:@0.404050:0.965315:0.836500:0.965315:0.836500:0.953363:0.404050:0.953363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 DBA 4 (Ev. 3) Representa e interpreta situaciones de ampliación y reducción en contextos diversos.:@0.404050:0.977418:0.920797:0.977418:0.920797:0.965466:0.404050:0.965466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a 6 cm:@0.832482:0.423972:0.881343:0.423972:0.881343:0.407479:0.832482:0.407479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4,5 cm:@0.832298:0.456428:0.880955:0.456428:0.880955:0.439935:0.832298:0.439935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 15 cm:@0.805623:0.295505:0.841977:0.295505:0.841977:0.282311:0.805623:0.282311:0.000000:0.000000:0.000000:0.000000:0.000000 6 cm:@0.890804:0.343448:0.919947:0.343448:0.919947:0.330254:0.890804:0.330254:0.000000:0.000000:0.000000:0.000000 9 cm:@0.889183:0.324515:0.889183:0.302558:0.871671:0.302558:0.871671:0.324515:0.000000:0.000000:0.000000:0.000000 7 cm:@0.138110:0.934213:0.172720:0.934213:0.172720:0.918544:0.138110:0.918544:0.000000:0.000000:0.000000:0.000000 18 cm:@0.139106:0.888250:0.182280:0.888250:0.182280:0.872581:0.139106:0.872581:0.000000:0.000000:0.000000:0.000000:0.000000 18 cm:@0.096213:0.726629:0.139387:0.726629:0.139387:0.710960:0.096213:0.710960:0.000000:0.000000:0.000000:0.000000:0.000000 18 cm:@0.140142:0.570304:0.183316:0.570439:0.183402:0.554770:0.140228:0.554636:0.000000:0.000000:0.000000:0.000000:0.000000 7 cm:@0.103705:0.589906:0.138314:0.590014:0.138400:0.574345:0.103791:0.574237:0.000000:0.000000:0.000000:0.000000 7 cm:@0.093741:0.563085:0.093884:0.537010:0.073087:0.536946:0.072944:0.563020:0.000000:0.000000:0.000000:0.000000 a:@0.188469:0.718501:0.196437:0.718501:0.196437:0.702832:0.188469:0.702832:0.000000 3,5 cm:@0.156808:0.793209:0.203036:0.793209:0.203036:0.777540:0.156808:0.777540:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3,5 cm:@0.179724:0.916437:0.225952:0.916437:0.225952:0.900768:0.179724:0.900768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 18 cm:@0.151616:0.379487:0.187642:0.379487:0.187642:0.366412:0.151616:0.366412:0.000000:0.000000:0.000000:0.000000:0.000000 7 cm:@0.193433:0.410696:0.222312:0.410696:0.222312:0.397622:0.193433:0.397622:0.000000:0.000000:0.000000:0.000000 7 cm:@0.133844:0.430313:0.162723:0.430313:0.162723:0.417239:0.133844:0.417239:0.000000:0.000000:0.000000:0.000000 6 cm:@0.131254:0.210362:0.163831:0.210362:0.163831:0.195613:0.131254:0.195613:0.000000:0.000000:0.000000:0.000000 9 cm:@0.110758:0.231566:0.143335:0.231566:0.143335:0.216818:0.110758:0.216818:0.000000:0.000000:0.000000:0.000000 15 cm:@0.230509:0.208466:0.271148:0.208466:0.271148:0.193718:0.230509:0.193718:0.000000:0.000000:0.000000:0.000000:0.000000 Empaque 1:@0.127534:0.136836:0.210809:0.136836:0.210809:0.120402:0.127534:0.120402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Empaque 2:@0.127534:0.277891:0.210809:0.277891:0.210809:0.261457:0.127534:0.261457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000