{"id":943,"date":"2020-08-09T19:38:53","date_gmt":"2020-08-09T17:38:53","guid":{"rendered":"http:\/\/matma.com.pl\/?p=943"},"modified":"2020-08-15T21:24:31","modified_gmt":"2020-08-15T19:24:31","slug":"pole-powierzchni-i-jego-jednostki","status":"publish","type":"post","link":"http:\/\/matma.com.pl\/?p=943","title":{"rendered":"Pole powierzchni i jego jednostki"},"content":{"rendered":"<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Aby, zmierzy\u0107 d\u0142ugo\u015b\u0107 odcinka, czy odleg\u0142o\u015bci, pos\u0142ugujemy si\u0119 na linijk\u0105, metrem lub czymkolwiek innym, co s\u0142u\u017cy do mierzenia. A co, je\u015bli musimy obliczy\u0107 pole powierzchni dowolnej figury? Co to jest tak naprawd\u0119 pole powierzchni? I w jakich jednostkach si\u0119 je podaje?<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #4472c4;\">Obliczanie pola powierzchni<\/span> polega na podaniu, ile jednostkowych kwadracik\u00f3w (kwadrat\u00f3w o boku d\u0142ugo\u015bci jednej jednostki) jest potrzebnych do pokrycia ca\u0142ej figury.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Na przyk\u0142ad:<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\" wp-image-951 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-pow-300x253.png\" alt=\"\" width=\"194\" height=\"164\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-pow-300x253.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/pole-pow.png 354w\" sizes=\"(max-width: 194px) 100vw, 194px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">pole powierzchni tej figury wynosi 7 jednostek (mamy 7 kwadracik\u00f3w jednostkowych).<\/span><\/p>\n<p><span style=\"text-decoration: underline;\"><span style=\"font-family: 'book antiqua', palatino, serif;\">Najwa\u017cniejsze, \u017ceby nie myli\u0107 pola powierzchni z obwodem!<\/span><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"> Pole, czyli interesuje nas ca\u0142a powierzchnia figury, a je\u015bli chodzi o obw\u00f3d, to mamy na my\u015bli &#8222;otoczk\u0119&#8221; figury (kolor br\u0105zowy na rysunku).\u00a0<\/span><\/p>\n<p><span style=\"text-decoration: underline; font-family: 'book antiqua', palatino, serif;\">Jednostki d\u0142ugo\u015bci jakie znamy:<\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">milimetr <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1&amp;space;\\,&amp;space;mm\" alt=\"1 \\, mm\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">centymetr <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1&amp;space;\\,&amp;space;cm=10\\,&amp;space;mm\" alt=\"1 \\, cm=10\\, mm\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">decymetr <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;dm=10\\,&amp;space;cm=100\\,&amp;space;mm\" alt=\"1\\, dm=10\\, cm=100\\, mm\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">metr <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;m=10\\,&amp;space;dm=100\\,&amp;space;cm=1000\\,&amp;space;mm\" alt=\"1\\, m=10\\, dm=100\\, cm=1000\\, mm\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">kilometr <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;km=1000\\,&amp;space;m=10\\,&amp;space;000\\,&amp;space;dm=100\\,&amp;space;000\\,&amp;space;cm=1\\,&amp;space;000\\,&amp;space;000\\,&amp;space;mm\" alt=\"1\\, km=1000\\, m=10\\, 000\\, dm=100\\, 000\\, cm=1\\, 000\\, 000\\, mm\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"text-decoration: underline;\">Jednostki, w jakich podajemy pole powierzchni to<\/span>:<\/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\" \/>, to pole kwadratu o boku <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\" \/>), <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;cm^{2}\" alt=\"1\\, cm^{2}\" align=\"absmiddle\" \/> to pole kwadratu o boku <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\" \/>), <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;dm^{2}\" alt=\"1\\, dm^{2}\" align=\"absmiddle\" \/> to pole kwadratu o boku <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\" \/>), <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;m^{2}\" alt=\"1\\, m^{2}\" align=\"absmiddle\" \/> to pole kwadratu o boku <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\" \/>), <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;km^{2}\" alt=\"1\\, km^{2}\" align=\"absmiddle\" \/> to pole kwadratu o boku <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?1\\,&amp;space;km\" alt=\"1\\, km\" align=\"absmiddle\" \/><\/span><\/li>\n<\/ul>\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, wcale 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><span style=\"font-family: 'book antiqua', palatino, serif;\">Do okre\u015blania powierzchni w Polsce u\u017cywamy jeszcze, takich jednostek jak:<\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><strong><span style=\"color: #4472c4;\">ar<\/span><\/strong> &#8211; jednostka najcz\u0119\u015bciej stosowana w rolnictwie i geodezji. 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 <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 style=\"text-align: center;\"><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" 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;\"><strong><span style=\"color: #4472c4;\">hektar<\/span><\/strong> &#8211; jednostka najcz\u0119\u015bciej stosowana w rolnictwie i geodezji. Hektar oznaczamy symbolem <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?ha\" alt=\"ha\" align=\"absmiddle\" \/> i jest to pole powierzchni kwadratu o boku <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 style=\"text-align: center;\"><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" 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 style=\"text-align: center;\"><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" 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","protected":false},"excerpt":{"rendered":"<p>Aby, zmierzy\u0107 d\u0142ugo\u015b\u0107 odcinka, czy odleg\u0142o\u015bci, pos\u0142ugujemy si\u0119 na linijk\u0105, metrem lub czymkolwiek innym, co s\u0142u\u017cy do mierzenia. A co, je\u015bli musimy obliczy\u0107 pole powierzchni dowolnej figury? Co to jest tak naprawd\u0119 pole powierzchni? I w jakich jednostkach si\u0119 je podaje? Obliczanie pola powierzchni polega na podaniu, ile jednostkowych kwadracik\u00f3w (kwadrat\u00f3w o boku d\u0142ugo\u015bci jednej [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,12],"tags":[],"class_list":["post-943","post","type-post","status-publish","format-standard","hentry","category-baza-wiedzy","category-klasa-v"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Pole powierzchni i jego jednostki - 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=943\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pole powierzchni i jego jednostki - Matma.com.pl\" \/>\n<meta property=\"og:description\" content=\"Aby, zmierzy\u0107 d\u0142ugo\u015b\u0107 odcinka, czy odleg\u0142o\u015bci, pos\u0142ugujemy si\u0119 na linijk\u0105, metrem lub czymkolwiek innym, co s\u0142u\u017cy do mierzenia. A co, je\u015bli musimy obliczy\u0107 pole powierzchni dowolnej figury? Co to jest tak naprawd\u0119 pole powierzchni? I w jakich jednostkach si\u0119 je podaje? 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