{"id":1247,"date":"2020-08-15T21:21:22","date_gmt":"2020-08-15T19:21:22","guid":{"rendered":"http:\/\/matma.com.pl\/?p=1247"},"modified":"2020-08-25T20:04:50","modified_gmt":"2020-08-25T18:04:50","slug":"pola-wielokatow-2","status":"publish","type":"post","link":"http:\/\/matma.com.pl\/?p=1247","title":{"rendered":"Pola wielok\u0105t\u00f3w"},"content":{"rendered":"<p>Przypomnijmy<span style=\"font-family: 'book antiqua', palatino, serif;\"> sobie jakie jednostki s\u0142u\u017c\u0105 do okre\u015blania pola powierzchni. S\u0105 to:<\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">milimetry kwadratowe (<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?mm^{2}\" alt=\"mm^{2}\" align=\"absmiddle\" \/>) , <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;mm^{2}\" alt=\"1\\, mm^{2}\" align=\"absmiddle\" \/>\u00a0to pole kwadratu o boku\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;mm\" alt=\"1\\, mm\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">centymetry kwadratowe (<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?cm^{2}\" alt=\"cm^{2}\" align=\"absmiddle\" \/>),\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;cm^{2}\" alt=\"1\\, cm^{2}\" align=\"absmiddle\" \/>\u00a0to pole kwadratu o boku\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;cm\" alt=\"1\\, cm\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">decymetry kwadratowe (<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?dm^{2}\" alt=\"dm^{2}\" align=\"absmiddle\" \/>),\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;dm^{2}\" alt=\"1\\, dm^{2}\" align=\"absmiddle\" \/>\u00a0to pole kwadratu o boku\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;dm\" alt=\"1\\, dm\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">metry kwadratowe (<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?m^{2}\" alt=\"m^{2}\" align=\"absmiddle\" \/>),\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;m^{2}\" alt=\"1\\, m^{2}\" align=\"absmiddle\" \/>\u00a0to pole kwadratu o boku\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;m\" alt=\"1\\, m\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">kilometry kwadratowe (<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?km^{2}\" alt=\"km^{2}\" align=\"absmiddle\" \/>),\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;km^{2}\" alt=\"1\\, km^{2}\" align=\"absmiddle\" \/>\u00a0to pole kwadratu o boku\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;km\" alt=\"1\\, km\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">ar oznaczamy symbolem <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a\" alt=\"a\" align=\"absmiddle\" \/>\u00a0 i jest to pole powierzchni kwadratu o boku\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?10\\,&amp;space;m\" alt=\"10\\, m\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;a=10\\,&amp;space;m\\cdot&amp;space;10\\,&amp;space;m=100\\,&amp;space;m^{2}\" alt=\"1\\, a=10\\, m\\cdot 10\\, m=100\\, m^{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">hektar oznaczamy symbolem <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?ha\" alt=\"ha\" align=\"absmiddle\" \/>\u00a0i jest to pole powierzchni kwadratu o boku\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?100\\,&amp;space;m\" alt=\"100\\, m\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;ha=100\\,&amp;space;m\\cdot&amp;space;100\\cdot&amp;space;m=10\\,&amp;space;000\\,&amp;space;m^{2}\" alt=\"1\\, ha=100\\, m\\cdot 100\\cdot m=10\\, 000\\, m^{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;ha=100\\,&amp;space;a\" alt=\"1\\, ha=100\\, a\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Aby zamieni\u0107 wi\u0119ksz\u0105 jednostk\u0119 pola na mniejsz\u0105 i si\u0119 przy tym nie pomyli\u0107 nie trzeba si\u0119 uczy\u0107 na pami\u0119\u0107. Wystarczy stosowa\u0107 zale\u017cno\u015bci jakie wyst\u0119puj\u0105 mi\u0119dzy jednostkami. Poni\u017cej kilka przyk\u0142adowych zamian:<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;m^{2=}(100\\,&amp;space;cm)^{2}=10\\,&amp;space;000cm^{2}\" alt=\"1\\, m^{2=}(100\\, cm)^{2}=10\\, 000cm^{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?5\\,&amp;space;dm^{2}=5\\cdot&amp;space;1\\,&amp;space;dm^{2}=5\\cdot&amp;space;(10\\,cm&amp;space;)^{2}=5\\cdot&amp;space;100\\,&amp;space;cm^{2}=500\\,&amp;space;cm^{2}\" alt=\"5\\, dm^{2}=5\\cdot 1\\, dm^{2}=5\\cdot (10\\,cm )^{2}=5\\cdot 100\\, cm^{2}=500\\, cm^{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?8\\,&amp;space;cm^{2}=8\\cdot&amp;space;1\\,&amp;space;cm^{2}=8\\cdot&amp;space;(10\\,&amp;space;mm^{2})=8\\cdot&amp;space;100\\,&amp;space;mm^{2}=800\\,&amp;space;mm^{2}\" alt=\"8\\, cm^{2}=8\\cdot 1\\, cm^{2}=8\\cdot (10\\, mm^{2})=8\\cdot 100\\, mm^{2}=800\\, mm^{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: 'book antiqua', palatino, serif;\"><strong>Pami\u0119tajmy, \u017ce istota matematyki polega na zrozumieniu istniej\u0105cych fakt\u00f3w, a nie na uczeniu si\u0119 na pami\u0119\u0107!<\/strong><\/span><\/p>\n<p><strong><span style=\"font-family: 'book antiqua', palatino, serif; color: #4472c4;\">Pole prostok\u0105ta<\/span><\/strong><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"wp-image-1252 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/prostok\u0105t-polee.png\" alt=\"\" width=\"226\" height=\"164\" \/><\/span><\/p>\n<p><span style=\"color: #4472c4;\"><strong><span style=\"font-family: 'book antiqua', palatino, serif;\">Pole kwadratu<\/span><\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <img decoding=\"async\" class=\"alignnone wp-image-1253\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/kwadrat-pole.png\" alt=\"\" width=\"168\" height=\"192\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <img decoding=\"async\" class=\"alignnone wp-image-1254\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/kwadrat-polee.png\" alt=\"\" width=\"144\" height=\"188\" \/><\/span><\/p>\n<p><strong><span style=\"color: #4472c4;\"><span style=\"font-family: 'book antiqua', palatino, serif;\">Pole r\u00f3wnoleg\u0142oboku<\/span><\/span><\/strong><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1255 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/r\u00f3wnoleg\u0142obok-polee-300x120.png\" alt=\"\" width=\"350\" height=\"140\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/r\u00f3wnoleg\u0142obok-polee-300x120.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/r\u00f3wnoleg\u0142obok-polee.png 467w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Sk\u0105d taki wz\u00f3r?<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">We\u017amy dowolny r\u00f3wnoleg\u0142obok i przetnijmy go wzd\u0142u\u017c jednej wysoko\u015bci<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1260 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-r\u00f3wnoleg\u0142oboku-konstrukcja-300x180.png\" alt=\"\" width=\"228\" height=\"137\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-r\u00f3wnoleg\u0142oboku-konstrukcja-300x180.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-r\u00f3wnoleg\u0142oboku-konstrukcja.png 331w\" sizes=\"(max-width: 228px) 100vw, 228px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Nast\u0119pnie z\u0142\u00f3\u017cmy nasze dwie cz\u0119\u015bci w prostok\u0105t.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1261 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-r\u00f3wnoleg\u0142oboku-konstrukcja1.png\" alt=\"\" width=\"188\" height=\"137\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Teraz widzimy sk\u0105d mamy wz\u00f3r na pole r\u00f3wnoleg\u0142oboku.<\/span><\/p>\n<p><span style=\"color: #4472c4;\"><strong><span style=\"font-family: 'book antiqua', palatino, serif;\">Pole rombu<\/span><\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1256\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/romb-polee.png\" alt=\"\" width=\"200\" height=\"179\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1257\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/romb-polee1.png\" alt=\"\" width=\"212\" height=\"200\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Sk\u0105d takie wzory?<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Pierwszy wz\u00f3r, mo\u017cna wyprowadzi\u0107 analogicznie, jak wz\u00f3r na pole r\u00f3wnoleg\u0142oboku. Zajmijmy si\u0119 drugim wzorem z przek\u0105tnymi rombu.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">We\u017amy dwa jednakowe romby i jeden z nich przetnijmy wzd\u0142u\u017c przek\u0105tnych<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1262 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-rombu-konstrukcja-300x104.png\" alt=\"\" width=\"431\" height=\"150\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-rombu-konstrukcja-300x104.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-rombu-konstrukcja.png 660w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Nast\u0119pnie z\u0142\u00f3\u017cmy prostok\u0105t z otrzymanych element\u00f3w<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1263 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-rombu-konstrukcja1-300x253.png\" alt=\"\" width=\"233\" height=\"197\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-rombu-konstrukcja1-300x253.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-rombu-konstrukcja1.png 347w\" sizes=\"(max-width: 233px) 100vw, 233px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">pole naszego prostok\u0105ta to <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P=d_{1}\\cdot&amp;space;d_{2}\" alt=\"P=d_{1}\\cdot d_{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Jednak, ze wzgl\u0119du na to, \u017ce mieli\u015bmy dwa romby otrzymane pole <\/span><span style=\"font-family: 'book antiqua', palatino, serif;\">dzielimy<\/span><span style=\"font-family: 'book antiqua', palatino, serif;\">\u00a0<\/span><span style=\"font-family: 'book antiqua', palatino, serif;\">na dwa. Czyli otrzymujemy <\/span><img decoding=\"async\" style=\"font-family: 'book antiqua', palatino, serif;\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P=\\frac{d_{1}\\cdot&amp;space;d_{2}}{2}\" alt=\"P=\\frac{d_{1}\\cdot d_{2}}{2}\" align=\"absmiddle\" \/><\/p>\n<p><span style=\"color: #4472c4;\"><strong><span style=\"font-family: 'book antiqua', palatino, serif;\">Pole tr\u00f3jk\u0105ta<\/span><\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1258 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/tr\u00f3jk\u0105t-pole-300x172.png\" alt=\"\" width=\"375\" height=\"215\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/tr\u00f3jk\u0105t-pole-300x172.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/tr\u00f3jk\u0105t-pole.png 523w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Je\u015bli we\u017amiemy dwa jednakowe tr\u00f3jk\u0105ty to mo\u017cemy je z\u0142o\u017cy\u0107 w r\u00f3wnoleg\u0142obok.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1267 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-tr\u00f3jk\u0105ta-konstrukcja-300x242.png\" alt=\"\" width=\"214\" height=\"173\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-tr\u00f3jk\u0105ta-konstrukcja-300x242.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-tr\u00f3jk\u0105ta-konstrukcja.png 334w\" sizes=\"(max-width: 214px) 100vw, 214px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1268 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-tr\u00f3jk\u0105ta-konstrukcja1-300x164.png\" alt=\"\" width=\"274\" height=\"150\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-tr\u00f3jk\u0105ta-konstrukcja1-300x164.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-tr\u00f3jk\u0105ta-konstrukcja1.png 475w\" sizes=\"(max-width: 274px) 100vw, 274px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Widzimy, \u017ce powsta\u0142 nam r\u00f3wnoleg\u0142obok, a obliczenie jego pola ju\u017c nie stanowi problemu <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P=a\\cdot&amp;space;h\" alt=\"P=a\\cdot h\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #4472c4;\"><strong><span style=\"font-family: 'book antiqua', palatino, serif;\">Pole trapezu<\/span><\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1259 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/trapez-pole-300x150.png\" alt=\"\" width=\"320\" height=\"160\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/trapez-pole-300x150.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/trapez-pole.png 483w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Podobnie jak z tr\u00f3jk\u0105tem, je\u015bli we\u017amiemy dwa jednakowe trapezy to mo\u017cemy je z\u0142o\u017cy\u0107 w r\u00f3wnoleg\u0142obok.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1269 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-trapezu-konstrukcja-300x197.png\" alt=\"\" width=\"229\" height=\"150\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-trapezu-konstrukcja-300x197.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-trapezu-konstrukcja.png 372w\" sizes=\"(max-width: 229px) 100vw, 229px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-1270 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-trapezu-konstrukcja1-300x140.png\" alt=\"\" width=\"300\" height=\"140\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-trapezu-konstrukcja1-300x140.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-trapezu-konstrukcja1.png 497w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Widzimy, \u017ce powsta\u0142 nam r\u00f3wnoleg\u0142obok o jednym boku d\u0142ugo\u015bci <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?a+b\" alt=\"a+b\" align=\"absmiddle\" \/> . Obliczenie jego pola ju\u017c nie stanowi problemu <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P=\\frac{\\left&amp;space;(a+b&amp;space;\\right&amp;space;)\\cdot&amp;space;h}{2}\" alt=\"P=\\frac{\\left (a+b \\right )\\cdot h}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #4472c4;\"><strong><span style=\"font-family: 'book antiqua', palatino, serif;\">Pole dowolnego wielok\u0105ta<\/span><\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Aby obliczy\u0107 pole dowolnego wielok\u0105ta nale\u017cy podzieli\u0107 go na znane przez nas wielok\u0105ty. Nast\u0119pnie obliczy\u0107 pola mniejszych wielok\u0105t\u00f3w i zsumowa\u0107 otrzymane pola.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Przypomnijmy sobie jakie jednostki s\u0142u\u017c\u0105 do okre\u015blania pola powierzchni. S\u0105 to: milimetry kwadratowe () , \u00a0to pole kwadratu o boku\u00a0 centymetry kwadratowe (),\u00a0\u00a0to pole kwadratu o boku\u00a0 decymetry kwadratowe (),\u00a0\u00a0to pole kwadratu o boku\u00a0 metry kwadratowe (),\u00a0\u00a0to pole kwadratu o boku\u00a0 kilometry kwadratowe (),\u00a0\u00a0to pole kwadratu o boku\u00a0 ar oznaczamy symbolem \u00a0 i jest to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,13],"tags":[],"class_list":["post-1247","post","type-post","status-publish","format-standard","hentry","category-baza-wiedzy","category-klasa-vi"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Pola wielok\u0105t\u00f3w - Matma.com.pl<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/matma.com.pl\/?p=1247\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pola wielok\u0105t\u00f3w - Matma.com.pl\" \/>\n<meta property=\"og:description\" content=\"Przypomnijmy sobie jakie jednostki s\u0142u\u017c\u0105 do okre\u015blania pola powierzchni. 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