POLIGONAIS _ POLÍGONOS-DIAGONAIS ( 7° série)
Autor: Mazé | Publicado: 2012-12-17T11:18:00-08:00


POLIGONAIS- Consideremos no plano um conjunto finito de segmentos sucessivamente consecutivos e com dois consecutivos não colineares (não na mesma reta)





























Nas figuras C &nbsp; e &nbsp;D vê-se que a origem da poligonal coincide com a sua extremidade ,tem-se então as poligonais fechadas ou POLIGONOS. As demais são chamadas poligonais abertas.
REGIÕES: &nbsp;externa &nbsp; &nbsp;e região interna





























PERÍMETRO - Numa poligonal ou num polígono a reunião dos lados chama-se perímetro.E a soma das medidas dos lados recebe o nome de medida do perímetro da poligonal ou do polígono.
POLÍGONO CONVEXO - possui vertices, angulos internos, angulos externos e diagonais.





















CLASSIFICAÇÃO DOS POLÍGONOS - Os polígonos se classificam segundo o numero de lados ou de angulos ( num poligono o numero de lados = numero de vertices= nº de angulos.
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; octógono =8 lados
triangulo = 3 lados &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;eneágono = 9 lados &nbsp; &nbsp;
quadrilátero= 4 lados &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; decágono = 10 lados
pentágono = 5 lados &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; undecágono = 11 lados &nbsp; 
hexágono = 6 lados &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; dodecágono = 12 lados
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;pentadecágono = 15 lados 
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;icoságono &nbsp; = 20 lados
NUMERO DE DIAGONAIS DE UM POLÍGONO &nbsp;- Para descobrir quantas diagonais tem um polígono usamos a seguinte fórmula &nbsp; &nbsp; &nbsp;d= n(n-3): 2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; d=diagonal &nbsp; &nbsp; n=numero de lado
&nbsp;assim um icoságono tem : &nbsp; &nbsp; 170 diagonais &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 

d = n ( n - 3 ) : 2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; d= 20( 20 - 3) : 2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; d= 170

Se voce tem o numero de diagonais e quer saber qual é o polígono &nbsp;substitua &nbsp; (d ) pelo numero de diagonais e resolva a equação.
&nbsp;exemplo &nbsp; &nbsp; &nbsp; d=170 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;170 = n (n-3) : 2
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;170.2 = n(n-3)
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 340 = n² - 3n &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; -n² +3n + 340 = 0 &nbsp; n'= -17 &nbsp; &nbsp; &nbsp;n''= 20 &nbsp; &nbsp; &nbsp; 

Portanto 20 é o numero de lados do polígono &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; V= 20